From fdae033b0c552e756c8e240d05f08a708ce97b97 Mon Sep 17 00:00:00 2001 From: snowykami Date: Thu, 29 Aug 2024 10:31:08 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20docs=20from=20@=20snowykami/mb?= =?UTF-8?q?cp@807a240c49cb926ea47e4587deee4f1cb04092b6=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 404.html | 2 +- api-ex.html | 2 +- api/index.html | 2 +- api/mp_math/angle.html | 42 +++++++------- api/mp_math/const.html | 2 +- api/mp_math/equation.html | 13 +++-- api/mp_math/index.html | 2 +- api/mp_math/line.html | 38 ++++++------ api/mp_math/mp_math_typing.html | 2 +- api/mp_math/plane.html | 40 ++++++------- api/mp_math/point.html | 18 +++--- api/mp_math/segment.html | 6 +- api/mp_math/utils.html | 20 +++---- api/mp_math/vector.html | 58 +++++++++---------- api/particle/index.html | 2 +- api/presets/index.html | 2 +- api/presets/model/index.html | 6 +- ...6o.js => api_mp_math_angle.md.eAy7w1HN.js} | 38 ++++++------ 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zht_api_mp_math_utils.md.CERv8c-M.lean.js} (57%) rename assets/{zht_api_mp_math_vector.md.CDyAXuJb.js => zht_api_mp_math_vector.md.BTWxlpB1.js} (69%) rename assets/{zht_api_mp_math_vector.md.CDyAXuJb.lean.js => zht_api_mp_math_vector.md.BTWxlpB1.lean.js} (85%) rename assets/{zht_api_presets_model_index.md.CrdAyyCM.js => zht_api_presets_model_index.md.SQ5PPdaL.js} (88%) rename assets/{zht_api_presets_model_index.md.CrdAyyCM.lean.js => zht_api_presets_model_index.md.SQ5PPdaL.lean.js} (86%) diff --git a/404.html b/404.html index a400403..b3be285 100644 --- a/404.html +++ b/404.html @@ -15,7 +15,7 @@
- + \ No newline at end of file diff --git a/api-ex.html b/api-ex.html index 54943b1..b324d9f 100644 --- a/api-ex.html +++ b/api-ex.html @@ -453,7 +453,7 @@ }

Page Frontmatter ​

{
   "outline": "deep"
 }

More ​

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

- + \ No newline at end of file diff --git a/api/index.html b/api/index.html index 3db62f8..053c8cd 100644 --- a/api/index.html +++ b/api/index.html @@ -18,7 +18,7 @@
MBCP docs

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

- + \ No newline at end of file diff --git a/api/mp_math/angle.html b/api/mp_math/angle.html index d7c3338..c00fd01 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -12,12 +12,12 @@ - + -
MBCP docs

简体中文

English
日本語
繁體中文

简体中文

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日本語
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Appearance

class Angle ​

class AnyAngle(Angle) ​

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

说明: 任意角度。

参数:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
说明: 任意角度。
参数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
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 ​
method complementary(self) -> AnyAngle ​
说明: 余角：两角的和为90°。
返回: 余角
源代码
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
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 ​
method supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码
python
@property
+    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
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 ​
method maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
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 ​
method sin(self) -> float ​
说明: 正弦值。
返回: 正弦值
源代码
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源代码
python
def __truediv__(self, other):
+    ...
method self / other ​
源代码
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/const.html b/api/mp_math/const.html
index 3bc63a8..395f005 100644
--- a/api/mp_math/const.html
+++ b/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html
index 976f0fb..507a126 100644
--- a/api/mp_math/equation.html
+++ b/api/mp_math/equation.html
@@ -12,14 +12,17 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
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:
+    
MBCP docs
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
参数:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    > [!warning]
+    > 目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
+
     Args:
         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)
@@ -56,7 +59,7 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -66,7 +69,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -79,7 +82,7 @@
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/index.html b/api/mp_math/index.html
index c7b1939..2d9f267 100644
--- a/api/mp_math/index.html
+++ b/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/line.html b/api/mp_math/line.html
index da4826f..6aff5e7 100644
--- a/api/mp_math/line.html
+++ b/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
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class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
  • other: 平行直线或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
  • other: 平行直线或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other: 另一条直线
返回: 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other: 另一条直线
返回: 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回: 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回: 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
  • t: 参数t
返回: 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
  • t: 参数t
返回: 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
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)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
  • other: 另一条直线
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
  • other: 另一条直线
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
  • other: 另一条直线
返回: 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
  • other: 另一条直线
返回: 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
  • point: 点
返回: 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
  • point: 点
返回: 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
  • other: 另一条直线
返回: 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
  • other: 另一条直线
返回: 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
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 ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
  • p1: 点1
  • p2: 点2
返回: 直线
源代码
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other: 另一条直线
返回: 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other: 另一条直线
返回: 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other:
源代码
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other:
源代码
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/mp_math_typing.html b/api/mp_math/mp_math_typing.html
index 31267b1..fc7b0f3 100644
--- a/api/mp_math/mp_math_typing.html
+++ b/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
var RealNumber = int | float ​
  • 类型: TypeAlias
  • 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

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html
index 215519b..c78966c 100644
--- a/api/mp_math/plane.html
+++ b/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
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繁體中文
Appearance
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
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
method approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other: 另一个平面
返回: 是否近似相等
源代码
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
  • other: 另一个平面或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
  • other: 另一个平面或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other: 另一个平面
返回: 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other: 另一个平面
返回: 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回: 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回: 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
  • point: 指定点
返回: 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
  • point: 指定点
返回: 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other: 另一个平面
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other: 另一个平面
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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 ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
参数:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源代码
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源代码
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源代码
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源代码
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源代码
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
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):
+    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
  • other:
返回: 不平行平面的交线，平面平行返回None
源代码
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/point.html b/api/mp_math/point.html
index ee5ea9a..2d71357 100644
--- a/api/mp_math/point.html
+++ b/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
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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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源代码
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
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)
method __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
  • other:
源代码
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
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)
method self - other: Point3 => Vector3 ​
说明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html
index 9a2a480..86e27bb 100644
--- a/api/mp_math/segment.html
+++ b/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html
index 360bd68..98971b7 100644
--- a/api/mp_math/utils.html
+++ b/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func clamp() -> float ​
说明: 区间限定函数
参数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
MBCP docs
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func clamp() -> float ​
说明: 区间限定函数
参数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,7 +28,7 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
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:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -38,7 +38,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = 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
func sign(x: float = False) -> str ​
说明: 获取数的符号。
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -51,7 +51,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = 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 ''
func sign_format(x: float = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -67,8 +67,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -78,10 +78,10 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html
index 97fedbc..48892f6 100644
--- a/api/mp_math/vector.html
+++ b/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回: 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回: 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
  • other:
返回: 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
  • other:
返回: 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • other: 另一个向量
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • other: 另一个向量
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
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 ​
method unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: 单位向量
源代码
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
+    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
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)}'")
method __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
  • other:
返回: 是否相等
源代码
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
+    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
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)}"')
method self - other: Point3 ​
说明: P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
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':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • other:
源代码
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -193,18 +193,18 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
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)}'")
method self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/particle/index.html b/api/particle/index.html
index b18f34e..d2e59e5 100644
--- a/api/particle/index.html
+++ b/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/index.html b/api/presets/index.html
index afc89e0..9dd76bc 100644
--- a/api/presets/index.html
+++ b/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/model/index.html b/api/presets/model/index.html
index 80028a4..cf38c7a 100644
--- a/api/presets/model/index.html
+++ b/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码
python
@staticmethod
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

-    
+    
     
   
 
\ No newline at end of file
diff --git a/assets/api_mp_math_angle.md.B8w0LP6o.js b/assets/api_mp_math_angle.md.eAy7w1HN.js
similarity index 65%
rename from assets/api_mp_math_angle.md.B8w0LP6o.js
rename to assets/api_mp_math_angle.md.eAy7w1HN.js
index 7b43490..42da5d6 100644
--- a/assets/api_mp_math_angle.md.B8w0LP6o.js
+++ b/assets/api_mp_math_angle.md.eAy7w1HN.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
说明: 任意角度。
参数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
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 ​
method complementary(self) -> AnyAngle ​
说明: 余角：两角的和为90°。
返回: 余角
源代码
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
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 ​
method supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码
python
@property
+    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
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 ​
method maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
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 ​
method sin(self) -> float ​
说明: 正弦值。
返回: 正弦值
源代码
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源代码
python
def __truediv__(self, other):
+    ...
method self / other ​
源代码
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/api_mp_math_angle.md.B8w0LP6o.lean.js b/assets/api_mp_math_angle.md.eAy7w1HN.lean.js
similarity index 100%
rename from assets/api_mp_math_angle.md.B8w0LP6o.lean.js
rename to assets/api_mp_math_angle.md.eAy7w1HN.lean.js
diff --git a/assets/api_mp_math_equation.md.Cn4Dbi_N.js b/assets/api_mp_math_equation.md.Cug6-NqN.js
similarity index 74%
rename from assets/api_mp_math_equation.md.Cn4Dbi_N.js
rename to assets/api_mp_math_equation.md.Cug6-NqN.js
index e6df063..f510992 100644
--- a/assets/api_mp_math_equation.md.Cn4Dbi_N.js
+++ b/assets/api_mp_math_equation.md.Cug6-NqN.js
@@ -1,6 +1,9 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
参数:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
参数:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    > [!warning]
+    > 目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
+
     Args:
         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)
@@ -37,7 +40,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -47,7 +50,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -59,4 +62,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.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))])
`,19),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,20),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
diff --git a/assets/api_mp_math_equation.md.Cn4Dbi_N.lean.js b/assets/api_mp_math_equation.md.Cug6-NqN.lean.js
similarity index 85%
rename from assets/api_mp_math_equation.md.Cn4Dbi_N.lean.js
rename to assets/api_mp_math_equation.md.Cug6-NqN.lean.js
index ab9b8a3..f4480bb 100644
--- a/assets/api_mp_math_equation.md.Cn4Dbi_N.lean.js
+++ b/assets/api_mp_math_equation.md.Cug6-NqN.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=n("",19),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=n("",20),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
diff --git a/assets/api_mp_math_line.md.B1jAKPr1.js b/assets/api_mp_math_line.md.DsJQDchM.js
similarity index 66%
rename from assets/api_mp_math_line.md.B1jAKPr1.js
rename to assets/api_mp_math_line.md.DsJQDchM.js
index bafac4e..b12a2f8 100644
--- a/assets/api_mp_math_line.md.B1jAKPr1.js
+++ b/assets/api_mp_math_line.md.DsJQDchM.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},t=n(`
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
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.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n(`
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
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)
method cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
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)
method cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
  • other: 平行直线或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
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.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other: 另一条直线
返回: 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
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
method cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回: 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
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))
method get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
  • t: 参数t
返回: 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
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
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
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)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
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)
method is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
  • other: 另一条直线
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
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)
method is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
  • other: 另一条直线
返回: 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
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)
method is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
  • point: 点
返回: 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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)
method is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
  • other: 另一条直线
返回: 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
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
method simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
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 ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
  • p1: 点1
  • p2: 点2
返回: 直线
源代码
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
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)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other: 另一条直线
返回: 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
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)
method __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other:
源代码
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_line.md.B1jAKPr1.lean.js b/assets/api_mp_math_line.md.DsJQDchM.lean.js
similarity index 70%
rename from assets/api_mp_math_line.md.B1jAKPr1.lean.js
rename to assets/api_mp_math_line.md.DsJQDchM.lean.js
index e425cef..56efe18 100644
--- a/assets/api_mp_math_line.md.B1jAKPr1.lean.js
+++ b/assets/api_mp_math_line.md.DsJQDchM.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},t=n("",105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n("",105),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_plane.md.DLB54RNP.js b/assets/api_mp_math_plane.md.CmoVvPiw.js
similarity index 75%
rename from assets/api_mp_math_plane.md.DLB54RNP.js
rename to assets/api_mp_math_plane.md.CmoVvPiw.js
index 832d1bf..20f083b 100644
--- a/assets/api_mp_math_plane.md.DLB54RNP.js
+++ b/assets/api_mp_math_plane.md.CmoVvPiw.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
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.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
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
method approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other: 另一个平面
返回: 是否近似相等
源代码
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
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
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
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)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
  • other: 另一个平面或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
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)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other: 另一个平面
返回: 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
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)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回: 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
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))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
  • point: 指定点
返回: 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
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)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other: 另一个平面
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
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 ​
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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 ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
参数:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源代码
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
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 ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源代码
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
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 ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源代码
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
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 ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源代码
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
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):
+    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
  • other:
返回: 不平行平面的交线，平面平行返回None
源代码
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
`,103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/api_mp_math_plane.md.DLB54RNP.lean.js b/assets/api_mp_math_plane.md.CmoVvPiw.lean.js
similarity index 100%
rename from assets/api_mp_math_plane.md.DLB54RNP.lean.js
rename to assets/api_mp_math_plane.md.CmoVvPiw.lean.js
diff --git a/assets/api_mp_math_point.md.BwXaSbuz.js b/assets/api_mp_math_point.md.ClJD85mP.js
similarity index 63%
rename from assets/api_mp_math_point.md.BwXaSbuz.js
rename to assets/api_mp_math_point.md.ClJD85mP.js
index e591140..c1f3ae7 100644
--- a/assets/api_mp_math_point.md.BwXaSbuz.js
+++ b/assets/api_mp_math_point.md.ClJD85mP.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源代码
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
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)
method __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
  • other:
源代码
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
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)
method self - other: Point3 => Vector3 ​
说明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
diff --git a/assets/api_mp_math_point.md.BwXaSbuz.lean.js b/assets/api_mp_math_point.md.ClJD85mP.lean.js
similarity index 100%
rename from assets/api_mp_math_point.md.BwXaSbuz.lean.js
rename to assets/api_mp_math_point.md.ClJD85mP.lean.js
diff --git a/assets/api_mp_math_segment.md.C6i78ST1.js b/assets/api_mp_math_segment.md.7jBtS4F1.js
similarity index 81%
rename from assets/api_mp_math_segment.md.C6i78ST1.js
rename to assets/api_mp_math_segment.md.7jBtS4F1.js
index 8e16b56..304bf09 100644
--- a/assets/api_mp_math_segment.md.C6i78ST1.js
+++ b/assets/api_mp_math_segment.md.7jBtS4F1.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
diff --git a/assets/api_mp_math_segment.md.C6i78ST1.lean.js b/assets/api_mp_math_segment.md.7jBtS4F1.lean.js
similarity index 100%
rename from assets/api_mp_math_segment.md.C6i78ST1.lean.js
rename to assets/api_mp_math_segment.md.7jBtS4F1.lean.js
diff --git a/assets/ja_api_mp_math_utils.md.CXGqGLUs.js b/assets/api_mp_math_utils.md.BMwtm7TJ.js
similarity index 69%
rename from assets/ja_api_mp_math_utils.md.CXGqGLUs.js
rename to assets/api_mp_math_utils.md.BMwtm7TJ.js
index 4f57e6f..6b2d37f 100644
--- a/assets/ja_api_mp_math_utils.md.CXGqGLUs.js
+++ b/assets/api_mp_math_utils.md.BMwtm7TJ.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
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.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),t={name:"api/mp_math/utils.md"},l=n(`
func clamp() -> float ​
说明: 区间限定函数
参数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,7 +9,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
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:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -19,7 +19,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
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
func sign(x: float = False) -> str ​
说明: 获取数的符号。
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
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 ''
func sign_format(x: float = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -48,8 +48,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -59,6 +59,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード
python
def __ne__(self, other):
-    return not self.__eq__(other)
`,33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码
python
def __ne__(self, other):
+    return not self.__eq__(other)
`,33),h=[l];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_utils.md.Bkx3QJ6f.lean.js b/assets/api_mp_math_utils.md.BMwtm7TJ.lean.js
similarity index 70%
rename from assets/api_mp_math_utils.md.Bkx3QJ6f.lean.js
rename to assets/api_mp_math_utils.md.BMwtm7TJ.lean.js
index 01c767a..e04783d 100644
--- a/assets/api_mp_math_utils.md.Bkx3QJ6f.lean.js
+++ b/assets/api_mp_math_utils.md.BMwtm7TJ.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n("",33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),t={name:"api/mp_math/utils.md"},l=n("",33),h=[l];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_vector.md.Efti6kdT.js b/assets/api_mp_math_vector.md.CROCIDXX.js
similarity index 70%
rename from assets/api_mp_math_vector.md.Efti6kdT.js
rename to assets/api_mp_math_vector.md.CROCIDXX.js
index a843701..46eb303 100644
--- a/assets/api_mp_math_vector.md.Efti6kdT.js
+++ b/assets/api_mp_math_vector.md.CROCIDXX.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
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.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
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])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回: 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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)
method cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
  • other:
返回: 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
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
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • other: 另一个向量
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
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)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
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 ​
method unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: 单位向量
源代码
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
+    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
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)}'")
method __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
  • other:
返回: 是否相等
源代码
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
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)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
+    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
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)}"')
method self - other: Point3 ​
说明: P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
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':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • other:
源代码
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
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)}'")
method self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_vector.md.Efti6kdT.lean.js b/assets/api_mp_math_vector.md.CROCIDXX.lean.js
similarity index 85%
rename from assets/api_mp_math_vector.md.Efti6kdT.lean.js
rename to assets/api_mp_math_vector.md.CROCIDXX.lean.js
index b68d55a..a26b965 100644
--- a/assets/api_mp_math_vector.md.Efti6kdT.lean.js
+++ b/assets/api_mp_math_vector.md.CROCIDXX.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_presets_model_index.md.DY6YMRqf.js b/assets/api_presets_model_index.md.DUZx13AW.js
similarity index 88%
rename from assets/api_presets_model_index.md.DY6YMRqf.js
rename to assets/api_presets_model_index.md.DUZx13AW.js
index 9110ab6..703cf6b 100644
--- a/assets/api_presets_model_index.md.DY6YMRqf.js
+++ b/assets/api_presets_model_index.md.DUZx13AW.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/api_presets_model_index.md.DY6YMRqf.lean.js b/assets/api_presets_model_index.md.DUZx13AW.lean.js
similarity index 85%
rename from assets/api_presets_model_index.md.DY6YMRqf.lean.js
rename to assets/api_presets_model_index.md.DUZx13AW.lean.js
index 433fffa..8d14981 100644
--- a/assets/api_presets_model_index.md.DY6YMRqf.lean.js
+++ b/assets/api_presets_model_index.md.DUZx13AW.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_angle.md.DxBe_g0o.js b/assets/en_api_mp_math_angle.md.BuhpKHnt.js
similarity index 65%
rename from assets/ja_api_mp_math_angle.md.DxBe_g0o.js
rename to assets/en_api_mp_math_angle.md.BuhpKHnt.js
index cb5c395..94ef475 100644
--- a/assets/ja_api_mp_math_angle.md.DxBe_g0o.js
+++ b/assets/en_api_mp_math_angle.md.BuhpKHnt.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),t={name:"ja/api/mp_math/angle.md"},e=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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.BV61Qrc0.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),t={name:"en/api/mp_math/angle.md"},e=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード
python
@property
+        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
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 ​
method supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
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 ​
method degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
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 ​
method minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
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 ​
method maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
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 ​
method sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
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 ​
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
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 ​
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
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 ​
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
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 ​
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
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 ​
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
ソースコード
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
ソースコード
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
+    ...
method self / other ​
Source code
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_angle.md.DmK_A9xI.lean.js b/assets/en_api_mp_math_angle.md.BuhpKHnt.lean.js
similarity index 57%
rename from assets/en_api_mp_math_angle.md.DmK_A9xI.lean.js
rename to assets/en_api_mp_math_angle.md.BuhpKHnt.lean.js
index 789df0d..89f6a58 100644
--- a/assets/en_api_mp_math_angle.md.DmK_A9xI.lean.js
+++ b/assets/en_api_mp_math_angle.md.BuhpKHnt.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},t=n("",78),l=[t];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(e,[["render",h]]);export{c as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),t={name:"en/api/mp_math/angle.md"},e=n("",78),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_equation.md.-GejNICN.js b/assets/en_api_mp_math_equation.md.YQDGr03a.js
similarity index 71%
rename from assets/ja_api_mp_math_equation.md.-GejNICN.js
rename to assets/en_api_mp_math_equation.md.YQDGr03a.js
index a68f6f8..6d6c7b2 100644
--- a/assets/ja_api_mp_math_equation.md.-GejNICN.js
+++ b/assets/en_api_mp_math_equation.md.YQDGr03a.js
@@ -1,6 +1,9 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
引数:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
Arguments:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    > [!warning]
+    > 目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
+
     Args:
         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)
@@ -37,7 +40,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -47,7 +50,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -59,4 +62,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.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))])
`,19),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,20),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{u as __pageData,F as default};
diff --git a/assets/en_api_mp_math_equation.md.DU8q_g4G.lean.js b/assets/en_api_mp_math_equation.md.YQDGr03a.lean.js
similarity index 86%
rename from assets/en_api_mp_math_equation.md.DU8q_g4G.lean.js
rename to assets/en_api_mp_math_equation.md.YQDGr03a.lean.js
index 31b29d2..b8aa112 100644
--- a/assets/en_api_mp_math_equation.md.DU8q_g4G.lean.js
+++ b/assets/en_api_mp_math_equation.md.YQDGr03a.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n("",19),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{u as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n("",20),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{u as __pageData,F as default};
diff --git a/assets/en_api_mp_math_line.md.BBlzflWh.js b/assets/en_api_mp_math_line.md.BEvxdWYQ.js
similarity index 65%
rename from assets/en_api_mp_math_line.md.BBlzflWh.js
rename to assets/en_api_mp_math_line.md.BEvxdWYQ.js
index 77205d2..4003bd5 100644
--- a/assets/en_api_mp_math_line.md.BBlzflWh.js
+++ b/assets/en_api_mp_math_line.md.BEvxdWYQ.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n(`
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n(`
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
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)
method cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
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)
method cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
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.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return: 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
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
method cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return: 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
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))
method get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
  • t: 参数t
Return: 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
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
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
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)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
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)
method is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
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)
method is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return: 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
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)
method is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
  • point: 点
Return: 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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)
method is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
  • other: 另一条直线
Return: 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
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
method simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
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 ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
  • p1: 点1
  • p2: 点2
Return: 直线
Source code
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
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)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other: 另一条直线
Return: 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
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)
method __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other:
Source code
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
diff --git a/assets/en_api_mp_math_line.md.BBlzflWh.lean.js b/assets/en_api_mp_math_line.md.BEvxdWYQ.lean.js
similarity index 100%
rename from assets/en_api_mp_math_line.md.BBlzflWh.lean.js
rename to assets/en_api_mp_math_line.md.BEvxdWYQ.lean.js
diff --git a/assets/ja_api_mp_math_plane.md.Cm4a8eqF.js b/assets/en_api_mp_math_plane.md.DUu9P3nM.js
similarity index 76%
rename from assets/ja_api_mp_math_plane.md.Cm4a8eqF.js
rename to assets/en_api_mp_math_plane.md.DUu9P3nM.js
index aafb9f5..16d8458 100644
--- a/assets/ja_api_mp_math_plane.md.Cm4a8eqF.js
+++ b/assets/en_api_mp_math_plane.md.DUu9P3nM.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
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.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
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
method approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other: 另一个平面
Return: 是否近似相等
Source code
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
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
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
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)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
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)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other: 另一个平面
Return: 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
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)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return: 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
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))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
  • point: 指定点
Return: 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
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)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
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 ​
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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 ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Arguments:
  • point: 平面上的一点
  • normal: 法向量
Return: 平面
Source code
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
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 ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Return: 平面
Source code
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
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 ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1: 直线1
  • l2: 直线2
Return: 平面
Source code
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
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 ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Return: 平面
Source code
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • other:
戻り値: 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • other:
Return: 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,103),t=[h];function p(e,k,r,d,o,E){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/en_api_mp_math_plane.md.cxytQLD4.lean.js b/assets/en_api_mp_math_plane.md.DUu9P3nM.lean.js
similarity index 85%
rename from assets/en_api_mp_math_plane.md.cxytQLD4.lean.js
rename to assets/en_api_mp_math_plane.md.DUu9P3nM.lean.js
index e48f76b..6043c0a 100644
--- a/assets/en_api_mp_math_plane.md.cxytQLD4.lean.js
+++ b/assets/en_api_mp_math_plane.md.DUu9P3nM.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=n("",103),t=[h];function p(e,k,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=n("",103),t=[h];function p(e,k,r,d,o,E){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/en_api_mp_math_point.md.CXQGh5Zt.js b/assets/en_api_mp_math_point.md.DMig0FI1.js
similarity index 63%
rename from assets/en_api_mp_math_point.md.CXQGh5Zt.js
rename to assets/en_api_mp_math_point.md.DMig0FI1.js
index 6a301ea..534c390 100644
--- a/assets/en_api_mp_math_point.md.CXQGh5Zt.js
+++ b/assets/en_api_mp_math_point.md.DMig0FI1.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
Source code
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
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)
method __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
  • other:
Source code
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
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)
method self - other: Point3 => Vector3 ​
Description: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
diff --git a/assets/en_api_mp_math_point.md.CXQGh5Zt.lean.js b/assets/en_api_mp_math_point.md.DMig0FI1.lean.js
similarity index 100%
rename from assets/en_api_mp_math_point.md.CXQGh5Zt.lean.js
rename to assets/en_api_mp_math_point.md.DMig0FI1.lean.js
diff --git a/assets/en_api_mp_math_segment.md.CxreVgqR.js b/assets/en_api_mp_math_segment.md.CcaokAF8.js
similarity index 81%
rename from assets/en_api_mp_math_segment.md.CxreVgqR.js
rename to assets/en_api_mp_math_segment.md.CcaokAF8.js
index f462604..9a9610c 100644
--- a/assets/en_api_mp_math_segment.md.CxreVgqR.js
+++ b/assets/en_api_mp_math_segment.md.CcaokAF8.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
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.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
diff --git a/assets/en_api_mp_math_segment.md.CxreVgqR.lean.js b/assets/en_api_mp_math_segment.md.CcaokAF8.lean.js
similarity index 100%
rename from assets/en_api_mp_math_segment.md.CxreVgqR.lean.js
rename to assets/en_api_mp_math_segment.md.CcaokAF8.lean.js
diff --git a/assets/api_mp_math_utils.md.Bkx3QJ6f.js b/assets/en_api_mp_math_utils.md.DZohqw2b.js
similarity index 63%
rename from assets/api_mp_math_utils.md.Bkx3QJ6f.js
rename to assets/en_api_mp_math_utils.md.DZohqw2b.js
index ea744a5..01cddac 100644
--- a/assets/api_mp_math_utils.md.Bkx3QJ6f.js
+++ b/assets/en_api_mp_math_utils.md.DZohqw2b.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
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.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),t={name:"en/api/mp_math/utils.md"},l=n(`
func clamp() -> float ​
Description: 区间限定函数
Arguments:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
Return: 限制后的值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,7 +9,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
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:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x: 数1
  • y: 数2
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -19,7 +19,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
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
func sign(x: float = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
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 ''
func sign_format(x: float = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -48,8 +48,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -59,6 +59,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码
python
def __ne__(self, other):
-    return not self.__eq__(other)
`,33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
+    return not self.__eq__(other)
`,33),h=[l];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_utils.md.aavLLFMy.lean.js b/assets/en_api_mp_math_utils.md.DZohqw2b.lean.js
similarity index 100%
rename from assets/en_api_mp_math_utils.md.aavLLFMy.lean.js
rename to assets/en_api_mp_math_utils.md.DZohqw2b.lean.js
diff --git a/assets/en_api_mp_math_vector.md.BvKJEw7_.js b/assets/en_api_mp_math_vector.md.Sd_IZsgE.js
similarity index 69%
rename from assets/en_api_mp_math_vector.md.BvKJEw7_.js
rename to assets/en_api_mp_math_vector.md.Sd_IZsgE.js
index 499c2be..26709e7 100644
--- a/assets/en_api_mp_math_vector.md.BvKJEw7_.js
+++ b/assets/en_api_mp_math_vector.md.Sd_IZsgE.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
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.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
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])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return: 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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)
method cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
  • other:
Return: 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
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
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
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)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
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 ​
method unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: 单位向量
Source code
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
+    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
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)}'")
method __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
  • other:
Return: 是否相等
Source code
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
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)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
+    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
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)}"')
method self - other: Point3 ​
Description: P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
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':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • other:
Source code
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
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)}'")
method self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量
`,125),e=[h];function l(p,k,r,o,d,E){return a(),i("div",null,e)}const F=s(n,[["render",l]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量
`,125),e=[h];function l(p,k,r,o,d,g){return a(),i("div",null,e)}const F=s(n,[["render",l]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_vector.md.BvKJEw7_.lean.js b/assets/en_api_mp_math_vector.md.Sd_IZsgE.lean.js
similarity index 85%
rename from assets/en_api_mp_math_vector.md.BvKJEw7_.lean.js
rename to assets/en_api_mp_math_vector.md.Sd_IZsgE.lean.js
index 0c06b93..6e6f85e 100644
--- a/assets/en_api_mp_math_vector.md.BvKJEw7_.lean.js
+++ b/assets/en_api_mp_math_vector.md.Sd_IZsgE.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t("",125),e=[h];function l(p,k,r,o,d,E){return a(),i("div",null,e)}const F=s(n,[["render",l]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t("",125),e=[h];function l(p,k,r,o,d,g){return a(),i("div",null,e)}const F=s(n,[["render",l]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_presets_model_index.md.DBfUZUBC.js b/assets/en_api_presets_model_index.md.Cs8vON2C.js
similarity index 86%
rename from assets/en_api_presets_model_index.md.DBfUZUBC.js
rename to assets/en_api_presets_model_index.md.Cs8vON2C.js
index 5e257f1..9fd5731 100644
--- a/assets/en_api_presets_model_index.md.DBfUZUBC.js
+++ b/assets/en_api_presets_model_index.md.Cs8vON2C.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_presets_model_index.md.DBfUZUBC.lean.js b/assets/en_api_presets_model_index.md.Cs8vON2C.lean.js
similarity index 58%
rename from assets/en_api_presets_model_index.md.DBfUZUBC.lean.js
rename to assets/en_api_presets_model_index.md.Cs8vON2C.lean.js
index 28f9d3a..dcdc11c 100644
--- a/assets/en_api_presets_model_index.md.DBfUZUBC.lean.js
+++ b/assets/en_api_presets_model_index.md.Cs8vON2C.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_angle.md.DmK_A9xI.js b/assets/ja_api_mp_math_angle.md.DL9J6RE2.js
similarity index 66%
rename from assets/en_api_mp_math_angle.md.DmK_A9xI.js
rename to assets/ja_api_mp_math_angle.md.DL9J6RE2.js
index 46d588d..bc97db1 100644
--- a/assets/en_api_mp_math_angle.md.DmK_A9xI.js
+++ b/assets/ja_api_mp_math_angle.md.DL9J6RE2.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},t=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),t={name:"ja/api/mp_math/angle.md"},e=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
python
@property
+        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
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 ​
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
python
@property
+    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
ソースコード
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
ソースコード
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
Source code
python
def __truediv__(self, other):
+    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[t];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(e,[["render",h]]);export{c as __pageData,F as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_angle.md.DxBe_g0o.lean.js b/assets/ja_api_mp_math_angle.md.DL9J6RE2.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_angle.md.DxBe_g0o.lean.js
rename to assets/ja_api_mp_math_angle.md.DL9J6RE2.lean.js
diff --git a/assets/en_api_mp_math_equation.md.DU8q_g4G.js b/assets/ja_api_mp_math_equation.md.tmRhsqm6.js
similarity index 77%
rename from assets/en_api_mp_math_equation.md.DU8q_g4G.js
rename to assets/ja_api_mp_math_equation.md.tmRhsqm6.js
index 5669c7c..db4cd31 100644
--- a/assets/en_api_mp_math_equation.md.DU8q_g4G.js
+++ b/assets/ja_api_mp_math_equation.md.tmRhsqm6.js
@@ -1,6 +1,9 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
Arguments:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
引数:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    > [!warning]
+    > 目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
+
     Args:
         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)
@@ -37,7 +40,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -47,7 +50,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -59,4 +62,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,19),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{u as __pageData,F as default};
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,20),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_equation.md.-GejNICN.lean.js b/assets/ja_api_mp_math_equation.md.tmRhsqm6.lean.js
similarity index 86%
rename from assets/ja_api_mp_math_equation.md.-GejNICN.lean.js
rename to assets/ja_api_mp_math_equation.md.tmRhsqm6.lean.js
index cef2091..4ded0f5 100644
--- a/assets/ja_api_mp_math_equation.md.-GejNICN.lean.js
+++ b/assets/ja_api_mp_math_equation.md.tmRhsqm6.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n("",19),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n("",20),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_line.md.CMfQT6TH.js b/assets/ja_api_mp_math_line.md.fj-_s5Ug.js
similarity index 66%
rename from assets/ja_api_mp_math_line.md.CMfQT6TH.js
rename to assets/ja_api_mp_math_line.md.fj-_s5Ug.js
index 701b590..7694534 100644
--- a/assets/ja_api_mp_math_line.md.CMfQT6TH.js
+++ b/assets/ja_api_mp_math_line.md.fj-_s5Ug.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},t=n(`
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
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.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),t={name:"ja/api/mp_math/line.md"},l=n(`
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
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)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
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)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
  • other: 平行直线或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
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.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値: 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
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
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値: 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
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))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
  • t: 参数t
戻り値: 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
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
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
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)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
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)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
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)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値: 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
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)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
  • point: 点
戻り値: 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
  • other: 另一条直线
戻り値: 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
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
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
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 ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
  • p1: 点1
  • p2: 点2
戻り値: 直线
ソースコード
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
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)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other: 另一条直线
戻り値: 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
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)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other:
ソースコード
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_line.md.CMfQT6TH.lean.js b/assets/ja_api_mp_math_line.md.fj-_s5Ug.lean.js
similarity index 57%
rename from assets/ja_api_mp_math_line.md.CMfQT6TH.lean.js
rename to assets/ja_api_mp_math_line.md.fj-_s5Ug.lean.js
index 8842389..f7adf8e 100644
--- a/assets/ja_api_mp_math_line.md.CMfQT6TH.lean.js
+++ b/assets/ja_api_mp_math_line.md.fj-_s5Ug.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},t=n("",105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),t={name:"ja/api/mp_math/line.md"},l=n("",105),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_plane.md.Buk-SLcC.js b/assets/ja_api_mp_math_plane.md.yLekgCvK.js
similarity index 75%
rename from assets/zht_api_mp_math_plane.md.Buk-SLcC.js
rename to assets/ja_api_mp_math_plane.md.yLekgCvK.js
index e958288..8f6ea20 100644
--- a/assets/zht_api_mp_math_plane.md.Buk-SLcC.js
+++ b/assets/ja_api_mp_math_plane.md.yLekgCvK.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
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.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
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
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other: 另一个平面
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
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
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
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)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
  • other: 另一个平面或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
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)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other: 另一个平面
戻り値: 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
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)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値: 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
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))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
  • point: 指定点
戻り値: 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
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)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
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 ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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 ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
引数:
  • point: 平面上的一点
  • normal: 法向量
戻り値: 平面
ソースコード
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
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 ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
戻り値: 平面
ソースコード
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
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 ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1: 直线1
  • l2: 直线2
戻り値: 平面
ソースコード
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
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 ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値: 平面
ソースコード
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • other:
返回: 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • other:
戻り値: 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
`,103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_plane.md.Cm4a8eqF.lean.js b/assets/ja_api_mp_math_plane.md.yLekgCvK.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_plane.md.Cm4a8eqF.lean.js
rename to assets/ja_api_mp_math_plane.md.yLekgCvK.lean.js
diff --git a/assets/ja_api_mp_math_point.md.CQAIjHfb.js b/assets/ja_api_mp_math_point.md.CpHHrSk8.js
similarity index 64%
rename from assets/ja_api_mp_math_point.md.CQAIjHfb.js
rename to assets/ja_api_mp_math_point.md.CpHHrSk8.js
index 89c98b5..8348b94 100644
--- a/assets/ja_api_mp_math_point.md.CQAIjHfb.js
+++ b/assets/ja_api_mp_math_point.md.CpHHrSk8.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
ソースコード
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
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)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
引数:
  • other:
ソースコード
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
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)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
diff --git a/assets/ja_api_mp_math_point.md.CQAIjHfb.lean.js b/assets/ja_api_mp_math_point.md.CpHHrSk8.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_point.md.CQAIjHfb.lean.js
rename to assets/ja_api_mp_math_point.md.CpHHrSk8.lean.js
diff --git a/assets/ja_api_mp_math_segment.md.D0U5bMSu.js b/assets/ja_api_mp_math_segment.md.CB1_z-rn.js
similarity index 81%
rename from assets/ja_api_mp_math_segment.md.D0U5bMSu.js
rename to assets/ja_api_mp_math_segment.md.CB1_z-rn.js
index 522a58c..c807dfc 100644
--- a/assets/ja_api_mp_math_segment.md.D0U5bMSu.js
+++ b/assets/ja_api_mp_math_segment.md.CB1_z-rn.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
diff --git a/assets/ja_api_mp_math_segment.md.D0U5bMSu.lean.js b/assets/ja_api_mp_math_segment.md.CB1_z-rn.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_segment.md.D0U5bMSu.lean.js
rename to assets/ja_api_mp_math_segment.md.CB1_z-rn.lean.js
diff --git a/assets/en_api_mp_math_utils.md.aavLLFMy.js b/assets/ja_api_mp_math_utils.md.BrfEEfl-.js
similarity index 65%
rename from assets/en_api_mp_math_utils.md.aavLLFMy.js
rename to assets/ja_api_mp_math_utils.md.BrfEEfl-.js
index 6cd6f3b..6ab1432 100644
--- a/assets/en_api_mp_math_utils.md.aavLLFMy.js
+++ b/assets/ja_api_mp_math_utils.md.BrfEEfl-.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),t={name:"en/api/mp_math/utils.md"},l=n(`
func clamp() -> 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.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),t={name:"ja/api/mp_math/utils.md"},l=n(`
func clamp() -> float ​
説明: 区间限定函数
引数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値: 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,7 +9,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
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:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -19,7 +19,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
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
func sign(x: float = False) -> str ​
説明: 获取数的符号。
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
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 ''
func sign_format(x: float = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -48,8 +48,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -59,6 +59,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
-    return not self.__eq__(other)
`,33),h=[l];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード
python
def __ne__(self, other):
+    return not self.__eq__(other)
`,33),h=[l];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_utils.md.CXGqGLUs.lean.js b/assets/ja_api_mp_math_utils.md.BrfEEfl-.lean.js
similarity index 57%
rename from assets/ja_api_mp_math_utils.md.CXGqGLUs.lean.js
rename to assets/ja_api_mp_math_utils.md.BrfEEfl-.lean.js
index 33263b4..b58e91e 100644
--- a/assets/ja_api_mp_math_utils.md.CXGqGLUs.lean.js
+++ b/assets/ja_api_mp_math_utils.md.BrfEEfl-.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n("",33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),t={name:"ja/api/mp_math/utils.md"},l=n("",33),h=[l];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_vector.md.C9TtayJk.js b/assets/ja_api_mp_math_vector.md.p54TKACE.js
similarity index 70%
rename from assets/ja_api_mp_math_vector.md.C9TtayJk.js
rename to assets/ja_api_mp_math_vector.md.p54TKACE.js
index ff942bd..9e30d60 100644
--- a/assets/ja_api_mp_math_vector.md.C9TtayJk.js
+++ b/assets/ja_api_mp_math_vector.md.p54TKACE.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
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.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
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])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値: 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
  • other:
戻り値: 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
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
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
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)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
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 ​
method length(self) -> float ​
説明: 向量的模。
戻り値: 模
ソースコード
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
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 ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: 单位向量
ソースコード
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
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)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
  • other:
戻り値: 是否相等
ソースコード
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
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)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
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)}"')
method self - other: Point3 ​
説明: P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
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':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • other:
ソースコード
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
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)}'")
method self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_vector.md.C9TtayJk.lean.js b/assets/ja_api_mp_math_vector.md.p54TKACE.lean.js
similarity index 85%
rename from assets/ja_api_mp_math_vector.md.C9TtayJk.lean.js
rename to assets/ja_api_mp_math_vector.md.p54TKACE.lean.js
index a9174df..78815d4 100644
--- a/assets/ja_api_mp_math_vector.md.C9TtayJk.lean.js
+++ b/assets/ja_api_mp_math_vector.md.p54TKACE.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_presets_model_index.md.DAVK1sDI.js b/assets/ja_api_presets_model_index.md.D8yZmO5R.js
similarity index 88%
rename from assets/ja_api_presets_model_index.md.DAVK1sDI.js
rename to assets/ja_api_presets_model_index.md.D8yZmO5R.js
index f234eaa..cec2b23 100644
--- a/assets/ja_api_presets_model_index.md.DAVK1sDI.js
+++ b/assets/ja_api_presets_model_index.md.D8yZmO5R.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/ja_api_presets_model_index.md.DAVK1sDI.lean.js b/assets/ja_api_presets_model_index.md.D8yZmO5R.lean.js
similarity index 86%
rename from assets/ja_api_presets_model_index.md.DAVK1sDI.lean.js
rename to assets/ja_api_presets_model_index.md.D8yZmO5R.lean.js
index 8f9992c..6239e6f 100644
--- a/assets/ja_api_presets_model_index.md.DAVK1sDI.lean.js
+++ b/assets/ja_api_presets_model_index.md.D8yZmO5R.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_angle.md._4N19GGe.js b/assets/zht_api_mp_math_angle.md.B4T6L25M.js
similarity index 66%
rename from assets/zht_api_mp_math_angle.md._4N19GGe.js
rename to assets/zht_api_mp_math_angle.md.B4T6L25M.js
index 7c2b91f..0fc8940 100644
--- a/assets/zht_api_mp_math_angle.md._4N19GGe.js
+++ b/assets/zht_api_mp_math_angle.md.B4T6L25M.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),t={name:"zht/api/mp_math/angle.md"},e=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),t={name:"zht/api/mp_math/angle.md"},e=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼
python
@property
+        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
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 ​
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
返回: 补角
源碼
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
返回: 弧度
源碼
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
返回: 弧度
源碼
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼
python
@property
+    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
返回: 正弦值
源碼
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
返回: 正弦值
源碼
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源碼
python
def __truediv__(self, other):
+    ...
method self / other ​
源碼
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_angle.md._4N19GGe.lean.js b/assets/zht_api_mp_math_angle.md.B4T6L25M.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_angle.md._4N19GGe.lean.js
rename to assets/zht_api_mp_math_angle.md.B4T6L25M.lean.js
diff --git a/assets/zht_api_mp_math_equation.md.MGSqd_Ep.js b/assets/zht_api_mp_math_equation.md.5p50czv3.js
similarity index 72%
rename from assets/zht_api_mp_math_equation.md.MGSqd_Ep.js
rename to assets/zht_api_mp_math_equation.md.5p50czv3.js
index c29835b..085f9de 100644
--- a/assets/zht_api_mp_math_equation.md.MGSqd_Ep.js
+++ b/assets/zht_api_mp_math_equation.md.5p50czv3.js
@@ -1,6 +1,9 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
變數説明:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
變數説明:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    > [!warning]
+    > 目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
+
     Args:
         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)
@@ -37,7 +40,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -47,7 +50,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -59,4 +62,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.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))])
`,19),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,20),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_equation.md.MGSqd_Ep.lean.js b/assets/zht_api_mp_math_equation.md.5p50czv3.lean.js
similarity index 86%
rename from assets/zht_api_mp_math_equation.md.MGSqd_Ep.lean.js
rename to assets/zht_api_mp_math_equation.md.5p50czv3.lean.js
index 7559bab..3a53c98 100644
--- a/assets/zht_api_mp_math_equation.md.MGSqd_Ep.lean.js
+++ b/assets/zht_api_mp_math_equation.md.5p50czv3.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n("",19),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n("",20),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{F as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_line.md.4ncoPmkZ.js b/assets/zht_api_mp_math_line.md.DYC1X0oD.js
similarity index 65%
rename from assets/zht_api_mp_math_line.md.4ncoPmkZ.js
rename to assets/zht_api_mp_math_line.md.DYC1X0oD.js
index 3242cf3..fb70858 100644
--- a/assets/zht_api_mp_math_line.md.4ncoPmkZ.js
+++ b/assets/zht_api_mp_math_line.md.DYC1X0oD.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},t=n(`
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
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.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),t={name:"zht/api/mp_math/line.md"},l=n(`
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
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)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other: 另一条直线
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
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)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
  • other: 平行直线或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
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.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回: 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
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
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
  • point: 指定点
返回: 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
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))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
  • t: 参数t
返回: 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
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
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
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)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
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)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
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)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回: 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
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)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
  • point: 点
返回: 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
  • other: 另一条直线
返回: 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
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
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
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 ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
  • p1: 点1
  • p2: 点2
返回: 直线
源碼
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
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)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other: 另一条直线
返回: 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
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)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other:
源碼
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_line.md.4ncoPmkZ.lean.js b/assets/zht_api_mp_math_line.md.DYC1X0oD.lean.js
similarity index 57%
rename from assets/zht_api_mp_math_line.md.4ncoPmkZ.lean.js
rename to assets/zht_api_mp_math_line.md.DYC1X0oD.lean.js
index 8d2d9e6..3bb8bdc 100644
--- a/assets/zht_api_mp_math_line.md.4ncoPmkZ.lean.js
+++ b/assets/zht_api_mp_math_line.md.DYC1X0oD.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},t=n("",105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),t={name:"zht/api/mp_math/line.md"},l=n("",105),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_plane.md.cxytQLD4.js b/assets/zht_api_mp_math_plane.md.B6GWRRF6.js
similarity index 76%
rename from assets/en_api_mp_math_plane.md.cxytQLD4.js
rename to assets/zht_api_mp_math_plane.md.B6GWRRF6.js
index 3d6016e..592fc51 100644
--- a/assets/en_api_mp_math_plane.md.cxytQLD4.js
+++ b/assets/zht_api_mp_math_plane.md.B6GWRRF6.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
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.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
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
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other: 另一个平面
返回: 是否近似相等
源碼
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
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
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
  • other: 另一个平面
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
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)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
  • other: 另一个平面或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
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)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other: 另一个平面
返回: 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
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)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回: 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
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))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
  • point: 指定点
返回: 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
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)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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 ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
變數説明:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源碼
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
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 ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源碼
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
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 ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源碼
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
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 ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源碼
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • other:
Return: 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • other:
返回: 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,103),t=[h];function p(e,k,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_plane.md.Buk-SLcC.lean.js b/assets/zht_api_mp_math_plane.md.B6GWRRF6.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_plane.md.Buk-SLcC.lean.js
rename to assets/zht_api_mp_math_plane.md.B6GWRRF6.lean.js
diff --git a/assets/zht_api_mp_math_point.md.Bb3tyGv-.js b/assets/zht_api_mp_math_point.md.Bm1IEwlI.js
similarity index 63%
rename from assets/zht_api_mp_math_point.md.Bb3tyGv-.js
rename to assets/zht_api_mp_math_point.md.Bm1IEwlI.js
index da6c851..52ae783 100644
--- a/assets/zht_api_mp_math_point.md.Bb3tyGv-.js
+++ b/assets/zht_api_mp_math_point.md.Bm1IEwlI.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源碼
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
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)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
  • other:
源碼
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
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)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
diff --git a/assets/zht_api_mp_math_point.md.Bb3tyGv-.lean.js b/assets/zht_api_mp_math_point.md.Bm1IEwlI.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_point.md.Bb3tyGv-.lean.js
rename to assets/zht_api_mp_math_point.md.Bm1IEwlI.lean.js
diff --git a/assets/zht_api_mp_math_segment.md.U_lS4vUA.js b/assets/zht_api_mp_math_segment.md.Bop8t2IE.js
similarity index 81%
rename from assets/zht_api_mp_math_segment.md.U_lS4vUA.js
rename to assets/zht_api_mp_math_segment.md.Bop8t2IE.js
index 4e078d7..69a3d5c 100644
--- a/assets/zht_api_mp_math_segment.md.U_lS4vUA.js
+++ b/assets/zht_api_mp_math_segment.md.Bop8t2IE.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
diff --git a/assets/zht_api_mp_math_segment.md.U_lS4vUA.lean.js b/assets/zht_api_mp_math_segment.md.Bop8t2IE.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_segment.md.U_lS4vUA.lean.js
rename to assets/zht_api_mp_math_segment.md.Bop8t2IE.lean.js
diff --git a/assets/zht_api_mp_math_utils.md.ig9jQkoA.js b/assets/zht_api_mp_math_utils.md.CERv8c-M.js
similarity index 64%
rename from assets/zht_api_mp_math_utils.md.ig9jQkoA.js
rename to assets/zht_api_mp_math_utils.md.CERv8c-M.js
index c0fd388..2f7a9f6 100644
--- a/assets/zht_api_mp_math_utils.md.ig9jQkoA.js
+++ b/assets/zht_api_mp_math_utils.md.CERv8c-M.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
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.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),t={name:"zht/api/mp_math/utils.md"},l=n(`
func clamp() -> float ​
説明: 区间限定函数
變數説明:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,7 +9,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
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:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
變數説明:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -19,7 +19,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
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
func sign(x: float = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
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 ''
func sign_format(x: float = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -48,8 +48,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -59,6 +59,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
-    return not self.__eq__(other)
`,33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
+    return not self.__eq__(other)
`,33),h=[l];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_utils.md.ig9jQkoA.lean.js b/assets/zht_api_mp_math_utils.md.CERv8c-M.lean.js
similarity index 57%
rename from assets/zht_api_mp_math_utils.md.ig9jQkoA.lean.js
rename to assets/zht_api_mp_math_utils.md.CERv8c-M.lean.js
index 32646d9..2a6f2c3 100644
--- a/assets/zht_api_mp_math_utils.md.ig9jQkoA.lean.js
+++ b/assets/zht_api_mp_math_utils.md.CERv8c-M.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},t=n("",33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),t={name:"zht/api/mp_math/utils.md"},l=n("",33),h=[l];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_vector.md.CDyAXuJb.js b/assets/zht_api_mp_math_vector.md.BTWxlpB1.js
similarity index 69%
rename from assets/zht_api_mp_math_vector.md.CDyAXuJb.js
rename to assets/zht_api_mp_math_vector.md.BTWxlpB1.js
index 9a1a703..6306e26 100644
--- a/assets/zht_api_mp_math_vector.md.CDyAXuJb.js
+++ b/assets/zht_api_mp_math_vector.md.BTWxlpB1.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
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.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
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])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回: 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
  • other:
返回: 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
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
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
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)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
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 ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
+    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
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)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
  • other:
返回: 是否相等
源碼
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
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)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
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)}"')
method self - other: Point3 ​
説明: P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
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':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • other:
源碼
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
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)}'")
method self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_vector.md.CDyAXuJb.lean.js b/assets/zht_api_mp_math_vector.md.BTWxlpB1.lean.js
similarity index 85%
rename from assets/zht_api_mp_math_vector.md.CDyAXuJb.lean.js
rename to assets/zht_api_mp_math_vector.md.BTWxlpB1.lean.js
index 38a3194..28e1cd9 100644
--- a/assets/zht_api_mp_math_vector.md.CDyAXuJb.lean.js
+++ b/assets/zht_api_mp_math_vector.md.BTWxlpB1.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_presets_model_index.md.CrdAyyCM.js b/assets/zht_api_presets_model_index.md.SQ5PPdaL.js
similarity index 88%
rename from assets/zht_api_presets_model_index.md.CrdAyyCM.js
rename to assets/zht_api_presets_model_index.md.SQ5PPdaL.js
index 0340a3a..dfc5749 100644
--- a/assets/zht_api_presets_model_index.md.CrdAyyCM.js
+++ b/assets/zht_api_presets_model_index.md.SQ5PPdaL.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/zht_api_presets_model_index.md.CrdAyyCM.lean.js b/assets/zht_api_presets_model_index.md.SQ5PPdaL.lean.js
similarity index 86%
rename from assets/zht_api_presets_model_index.md.CrdAyyCM.lean.js
rename to assets/zht_api_presets_model_index.md.SQ5PPdaL.lean.js
index 8e76554..6adfabc 100644
--- a/assets/zht_api_presets_model_index.md.CrdAyyCM.lean.js
+++ b/assets/zht_api_presets_model_index.md.SQ5PPdaL.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/en/api/index.html b/en/api/index.html
index 9914944..d23e7d9 100644
--- a/en/api/index.html
+++ b/en/api/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html
index 9d07d0b..aac9a9b 100644
--- a/en/api/mp_math/angle.html
+++ b/en/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
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简体中文
日本語
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English
简体中文
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class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
python
@property
+        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
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 ​
method supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
python
@property
+    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
Source code
python
def __truediv__(self, other):
+    ...
method self / other ​
Source code
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html
index 2689be7..7e53814 100644
--- a/en/api/mp_math/const.html
+++ b/en/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html
index acbde78..ab1c6a8 100644
--- a/en/api/mp_math/equation.html
+++ b/en/api/mp_math/equation.html
@@ -12,14 +12,17 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
Arguments:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    
MBCP docs
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
Arguments:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    > [!warning]
+    > 目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
+
     Args:
         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)
@@ -56,7 +59,7 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -66,7 +69,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -79,7 +82,7 @@
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html
index 551254d..18744e4 100644
--- a/en/api/mp_math/index.html
+++ b/en/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html
index 147d978..c170f70 100644
--- a/en/api/mp_math/line.html
+++ b/en/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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日本語
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English
简体中文
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class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
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class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return: 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return: 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return: 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return: 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
  • t: 参数t
Return: 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
  • t: 参数t
Return: 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
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)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return: 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return: 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
  • point: 点
Return: 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
  • point: 点
Return: 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
  • other: 另一条直线
Return: 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
  • other: 另一条直线
Return: 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
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 ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
  • p1: 点1
  • p2: 点2
Return: 直线
Source code
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other: 另一条直线
Return: 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other: 另一条直线
Return: 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other:
Source code
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other:
Source code
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

-    
+    
     
   
 
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diff --git a/en/api/mp_math/mp_math_typing.html b/en/api/mp_math/mp_math_typing.html
index b8e1636..65f0b38 100644
--- a/en/api/mp_math/mp_math_typing.html
+++ b/en/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
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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

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html
index b5e713d..8a0487b 100644
--- a/en/api/mp_math/plane.html
+++ b/en/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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简体中文
日本語
繁體中文
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简体中文
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
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日本語
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
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
method approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other: 另一个平面
Return: 是否近似相等
Source code
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other: 另一个平面
Return: 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other: 另一个平面
Return: 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return: 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return: 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
  • point: 指定点
Return: 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
  • point: 指定点
Return: 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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 ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Arguments:
  • point: 平面上的一点
  • normal: 法向量
Return: 平面
Source code
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Return: 平面
Source code
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Return: 平面
Source code
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1: 直线1
  • l2: 直线2
Return: 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1: 直线1
  • l2: 直线2
Return: 平面
Source code
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Return: 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Return: 平面
Source code
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
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):
+    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • other:
Return: 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

-    
+    
     
   
 
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diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html
index f7c46a7..41cf088 100644
--- a/en/api/mp_math/point.html
+++ b/en/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
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):
+    
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
Source code
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
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)
method __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
  • other:
Source code
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
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)
method self - other: Point3 => Vector3 ​
Description: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/segment.html b/en/api/mp_math/segment.html
index 18a3997..8b069d9 100644
--- a/en/api/mp_math/segment.html
+++ b/en/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html
index 5e3c700..44850e5 100644
--- a/en/api/mp_math/utils.html
+++ b/en/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func clamp() -> 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:
+    
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func clamp() -> float ​
Description: 区间限定函数
Arguments:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
Return: 限制后的值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,7 +28,7 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
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:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x: 数1
  • y: 数2
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -38,7 +38,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = 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
func sign(x: float = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -51,7 +51,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = 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 ''
func sign_format(x: float = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -67,8 +67,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -78,10 +78,10 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/vector.html b/en/api/mp_math/vector.html
index bf25036..e942af2 100644
--- a/en/api/mp_math/vector.html
+++ b/en/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
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
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return: 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return: 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
  • other:
Return: 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
  • other:
Return: 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
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 ​
method unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: 单位向量
Source code
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
+    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
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)}'")
method __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
  • other:
Return: 是否相等
Source code
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
+    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
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)}"')
method self - other: Point3 ​
Description: P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
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':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • other:
Source code
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -193,18 +193,18 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
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)}'")
method self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量

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diff --git a/en/api/particle/index.html b/en/api/particle/index.html
index 7690671..89d3a71 100644
--- a/en/api/particle/index.html
+++ b/en/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
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diff --git a/en/api/presets/index.html b/en/api/presets/index.html
index 5111229..26c4680 100644
--- a/en/api/presets/index.html
+++ b/en/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
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+    
     
   
 
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diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html
index ba4b9f3..e2b2ef9 100644
--- a/en/api/presets/model/index.html
+++ b/en/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code
python
@staticmethod
+    
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简体中文
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class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

-    
+    
     
   
 
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diff --git a/guide/index.html b/guide/index.html
index ff58711..35c6c69 100644
--- a/guide/index.html
+++ b/guide/index.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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开始不了一点 ​

-    
+    
     
   
 
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diff --git a/hashmap.json b/hashmap.json
index 60c9fd1..aabbd0a 100644
--- a/hashmap.json
+++ b/hashmap.json
@@ -1 +1 @@
-{"api-ex.md":"DOsKaL8H","api_index.md":"BvazTqTB","api_mp_math_angle.md":"B8w0LP6o","api_mp_math_const.md":"D9zs7__H","api_mp_math_equation.md":"Cn4Dbi_N","api_mp_math_index.md":"4P0hk6gb","api_mp_math_line.md":"B1jAKPr1","api_mp_math_mp_math_typing.md":"COrE_fd3","api_mp_math_plane.md":"DLB54RNP","api_mp_math_point.md":"BwXaSbuz","api_mp_math_segment.md":"C6i78ST1","api_mp_math_utils.md":"Bkx3QJ6f","api_mp_math_vector.md":"Efti6kdT","api_particle_index.md":"BRCSxC3e","api_presets_index.md":"Dl6Ss91J","api_presets_model_index.md":"DY6YMRqf","en_api_index.md":"Bgu-LD1B","en_api_mp_math_angle.md":"DmK_A9xI","en_api_mp_math_const.md":"D_Flpj8t","en_api_mp_math_equation.md":"DU8q_g4G","en_api_mp_math_index.md":"DrjDUYBY","en_api_mp_math_line.md":"BBlzflWh","en_api_mp_math_mp_math_typing.md":"CyXXFdS4","en_api_mp_math_plane.md":"cxytQLD4","en_api_mp_math_point.md":"CXQGh5Zt","en_api_mp_math_segment.md":"CxreVgqR","en_api_mp_math_utils.md":"aavLLFMy","en_api_mp_math_vector.md":"BvKJEw7_","en_api_particle_index.md":"CmC1QX5o","en_api_presets_index.md":"CZ5hl_7D","en_api_presets_model_index.md":"DBfUZUBC","guide_index.md":"BE2yloik","index.md":"BE1qChTt","ja_api_index.md":"4BnflFIm","ja_api_mp_math_angle.md":"DxBe_g0o","ja_api_mp_math_const.md":"CyaIJkFx","ja_api_mp_math_equation.md":"-GejNICN","ja_api_mp_math_index.md":"CSAMHYsB","ja_api_mp_math_line.md":"CMfQT6TH","ja_api_mp_math_mp_math_typing.md":"Bl5kyhpI","ja_api_mp_math_plane.md":"Cm4a8eqF","ja_api_mp_math_point.md":"CQAIjHfb","ja_api_mp_math_segment.md":"D0U5bMSu","ja_api_mp_math_utils.md":"CXGqGLUs","ja_api_mp_math_vector.md":"C9TtayJk","ja_api_particle_index.md":"E2YnH7EN","ja_api_presets_index.md":"ATGcHt9d","ja_api_presets_model_index.md":"DAVK1sDI","md-ex.md":"BX0WqOqv","zht_api_index.md":"Dq4XPUKZ","zht_api_mp_math_angle.md":"_4N19GGe","zht_api_mp_math_const.md":"B8uQOIr_","zht_api_mp_math_equation.md":"MGSqd_Ep","zht_api_mp_math_index.md":"D09y2ubg","zht_api_mp_math_line.md":"4ncoPmkZ","zht_api_mp_math_mp_math_typing.md":"DLx0IibM","zht_api_mp_math_plane.md":"Buk-SLcC","zht_api_mp_math_point.md":"Bb3tyGv-","zht_api_mp_math_segment.md":"U_lS4vUA","zht_api_mp_math_utils.md":"ig9jQkoA","zht_api_mp_math_vector.md":"CDyAXuJb","zht_api_particle_index.md":"kAm9VAEw","zht_api_presets_index.md":"BmouaEaT","zht_api_presets_model_index.md":"CrdAyyCM"}
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diff --git a/index.html b/index.html
index 8948c40..ef91fca 100644
--- a/index.html
+++ b/index.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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MBCP docs
More basic change particle
用于几何运算和粒子制作的库
快速开始
API文档
高可用性
通过简单的接口，实现了大部分几何运算和粒子制作的需求
高集成度
对numpy、scipy及sumpy进行了封装和集成，使脚本编写像使用Geogebra一样简单
内置预设
提供了大量的预设，包括常见的几何图形、粒子效果等，方便快速制作

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diff --git a/ja/api/index.html b/ja/api/index.html
index fa91241..a31ce57 100644
--- a/ja/api/index.html
+++ b/ja/api/index.html
@@ -18,7 +18,7 @@
   
   
     
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diff --git a/ja/api/mp_math/angle.html b/ja/api/mp_math/angle.html
index 884a3da..a6529a0 100644
--- a/ja/api/mp_math/angle.html
+++ b/ja/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
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+    
     
     
   
   
-    
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class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード
python
def __init__(self, value: float, is_radian: bool=False):
+    
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class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
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 ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
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 ​
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
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 ​
method degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
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 ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
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 ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
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 ​
method sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
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 ​
method cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
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 ​
method tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
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 ​
method cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
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 ​
method sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
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 ​
method csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
ソースコード
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
ソースコード
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
ソースコード
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
ソースコード
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
+    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/const.html b/ja/api/mp_math/const.html
index 9061a09..ff1573e 100644
--- a/ja/api/mp_math/const.html
+++ b/ja/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html
index 17c0e18..c68af43 100644
--- a/ja/api/mp_math/equation.html
+++ b/ja/api/mp_math/equation.html
@@ -12,14 +12,17 @@
     
     
     
-    
+    
     
     
   
   
-    
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
引数:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
引数:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    > [!warning]
+    > 目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
+
     Args:
         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)
@@ -56,7 +59,7 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -66,7 +69,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -79,7 +82,7 @@
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/index.html b/ja/api/mp_math/index.html
index 25802c3..73edead 100644
--- a/ja/api/mp_math/index.html
+++ b/ja/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html
index d9510df..055eaa7 100644
--- a/ja/api/mp_math/line.html
+++ b/ja/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
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class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
  • other: 平行直线或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
  • other: 平行直线或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値: 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値: 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値: 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値: 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
  • t: 参数t
戻り値: 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
  • t: 参数t
戻り値: 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
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)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値: 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値: 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
  • point: 点
戻り値: 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
  • point: 点
戻り値: 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
  • other: 另一条直线
戻り値: 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
  • other: 另一条直线
戻り値: 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
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 ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
  • p1: 点1
  • p2: 点2
戻り値: 直线
ソースコード
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other: 另一条直线
戻り値: 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other: 另一条直线
戻り値: 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other:
ソースコード
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other:
ソースコード
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/mp_math_typing.html b/ja/api/mp_math/mp_math_typing.html
index 83ec983..f3661f0 100644
--- a/ja/api/mp_math/mp_math_typing.html
+++ b/ja/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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
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

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html
index 7195266..9e57b66 100644
--- a/ja/api/mp_math/plane.html
+++ b/ja/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
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Appearance
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
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
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other: 另一个平面
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
  • other: 另一个平面或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
  • other: 另一个平面或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other: 另一个平面
戻り値: 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other: 另一个平面
戻り値: 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値: 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値: 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
  • point: 指定点
戻り値: 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
  • point: 指定点
戻り値: 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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 ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
引数:
  • point: 平面上的一点
  • normal: 法向量
戻り値: 平面
ソースコード
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
戻り値: 平面
ソースコード
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
戻り値: 平面
ソースコード
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1: 直线1
  • l2: 直线2
戻り値: 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1: 直线1
  • l2: 直线2
戻り値: 平面
ソースコード
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値: 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値: 平面
ソースコード
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
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):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • other:
戻り値: 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/point.html b/ja/api/mp_math/point.html
index 15f6dad..a3126d1 100644
--- a/ja/api/mp_math/point.html
+++ b/ja/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+    
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
ソースコード
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
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)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
引数:
  • other:
ソースコード
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
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)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html
index c1a9a42..79251f0 100644
--- a/ja/api/mp_math/segment.html
+++ b/ja/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html
index 3daceaf..5916786 100644
--- a/ja/api/mp_math/utils.html
+++ b/ja/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func clamp() -> float ​
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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func clamp() -> float ​
説明: 区间限定函数
引数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値: 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,7 +28,7 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
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:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -38,7 +38,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = 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
func sign(x: float = False) -> str ​
説明: 获取数的符号。
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -51,7 +51,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = 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 ''
func sign_format(x: float = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -67,8 +67,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -78,10 +78,10 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html
index 4b7b445..7e38615 100644
--- a/ja/api/mp_math/vector.html
+++ b/ja/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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日本語
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値: 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値: 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
  • other:
戻り値: 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
  • other:
戻り値: 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
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 ​
method length(self) -> float ​
説明: 向量的模。
戻り値: 模
ソースコード
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
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 ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: 单位向量
ソースコード
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
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)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
  • other:
戻り値: 是否相等
ソースコード
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
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)}"')
method self - other: Point3 ​
説明: P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
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':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • other:
ソースコード
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -193,18 +193,18 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
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)}'")
method self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html
index 558924a..7390b96 100644
--- a/ja/api/particle/index.html
+++ b/ja/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html
index 020f74a..c5e598a 100644
--- a/ja/api/presets/index.html
+++ b/ja/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html
index c509dc3..e86d806 100644
--- a/ja/api/presets/model/index.html
+++ b/ja/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード
python
@staticmethod
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

-    
+    
     
   
 
\ No newline at end of file
diff --git a/md-ex.html b/md-ex.html
index 8ce2e4b..577f142 100644
--- a/md-ex.html
+++ b/md-ex.html
@@ -50,7 +50,7 @@
 ::: details
 This is a details block.
 :::
Output
INFO
This is an info box.
TIP
This is a tip.
WARNING
This is a warning.
DANGER
This is a dangerous warning.
Details
This is a details block.
More ​
Check out the documentation for the full list of markdown extensions.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/index.html b/zht/api/index.html
index d9da8e8..02b1c23 100644
--- a/zht/api/index.html
+++ b/zht/api/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/angle.html b/zht/api/mp_math/angle.html
index 2a124b9..e6c28e9 100644
--- a/zht/api/mp_math/angle.html
+++ b/zht/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼
python
@property
+        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
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 ​
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
返回: 补角
源碼
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
返回: 弧度
源碼
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
返回: 弧度
源碼
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼
python
@property
+    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
返回: 正弦值
源碼
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
返回: 正弦值
源碼
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源碼
python
def __truediv__(self, other):
+    ...
method self / other ​
源碼
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
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diff --git a/zht/api/mp_math/const.html b/zht/api/mp_math/const.html
index 3eb0bcc..eae6c25 100644
--- a/zht/api/mp_math/const.html
+++ b/zht/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/equation.html b/zht/api/mp_math/equation.html
index 9c1287a..0b2c29c 100644
--- a/zht/api/mp_math/equation.html
+++ b/zht/api/mp_math/equation.html
@@ -12,14 +12,17 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
變數説明:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    
MBCP docs
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繁體中文
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English
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
變數説明:
  • func: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
+    > [!warning]
+    > 目前数学界对于数值微分的稳定性问题还没有很好的解决方案，因此这个函数的稳定性也不是很好。
+
     Args:
         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)
@@ -56,7 +59,7 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+        raise ValueError('Invalid var type')
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -66,7 +69,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -79,7 +82,7 @@
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/index.html b/zht/api/mp_math/index.html
index 3c8528c..73bb453 100644
--- a/zht/api/mp_math/index.html
+++ b/zht/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/line.html b/zht/api/mp_math/line.html
index 5d7f851..7aa91a4 100644
--- a/zht/api/mp_math/line.html
+++ b/zht/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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简体中文
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class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
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class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other: 另一条直线
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other: 另一条直线
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
  • other: 平行直线或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
  • other: 平行直线或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回: 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回: 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
  • point: 指定点
返回: 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
  • point: 指定点
返回: 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
  • t: 参数t
返回: 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
  • t: 参数t
返回: 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
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)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回: 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回: 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
  • point: 点
返回: 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
  • point: 点
返回: 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
  • other: 另一条直线
返回: 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
  • other: 另一条直线
返回: 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
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 ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
  • p1: 点1
  • p2: 点2
返回: 直线
源碼
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other: 另一条直线
返回: 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other: 另一条直线
返回: 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other:
源碼
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other:
源碼
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/mp_math_typing.html b/zht/api/mp_math/mp_math_typing.html
index b5f2010..f871790 100644
--- a/zht/api/mp_math/mp_math_typing.html
+++ b/zht/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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简体中文
English
日本語
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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

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/plane.html b/zht/api/mp_math/plane.html
index 93c99bf..c750250 100644
--- a/zht/api/mp_math/plane.html
+++ b/zht/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
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
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other: 另一个平面
返回: 是否近似相等
源碼
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
  • other: 另一个平面
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
  • other: 另一个平面
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
  • other: 另一个平面或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
  • other: 另一个平面或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other: 另一个平面
返回: 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other: 另一个平面
返回: 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回: 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回: 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
  • point: 指定点
返回: 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
  • point: 指定点
返回: 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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 ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
變數説明:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源碼
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源碼
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源碼
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源碼
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源碼
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
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):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • other:
返回: 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html
index 9f80feb..3ea19c6 100644
--- a/zht/api/mp_math/point.html
+++ b/zht/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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繁體中文
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源碼
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
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)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
  • other:
源碼
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
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)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/segment.html b/zht/api/mp_math/segment.html
index 0a16cdf..c161f8a 100644
--- a/zht/api/mp_math/segment.html
+++ b/zht/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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繁體中文
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
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English
日本語
繁體中文
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html
index ac841c8..cad97d7 100644
--- a/zht/api/mp_math/utils.html
+++ b/zht/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
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日本語
繁體中文
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func clamp() -> float ​
説明: 区间限定函数
變數説明:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
MBCP docs
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func clamp() -> float ​
説明: 区间限定函数
變數説明:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,7 +28,7 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
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:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
變數説明:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -38,7 +38,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = 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
func sign(x: float = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -51,7 +51,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = 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 ''
func sign_format(x: float = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -67,8 +67,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -78,10 +78,10 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html
index 92a6df9..4166fa4 100644
--- a/zht/api/mp_math/vector.html
+++ b/zht/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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日本語
繁體中文
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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日本語
繁體中文
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Appearance
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回: 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回: 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
  • other:
返回: 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
  • other:
返回: 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
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 ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
+    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
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)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
  • other:
返回: 是否相等
源碼
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
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)}"')
method self - other: Point3 ​
説明: P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
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':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • other:
源碼
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -193,18 +193,18 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
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)}'")
method self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html
index a451923..5d9221f 100644
--- a/zht/api/particle/index.html
+++ b/zht/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/presets/index.html b/zht/api/presets/index.html
index d944da4..58245ee 100644
--- a/zht/api/presets/index.html
+++ b/zht/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html
index 758f498..929eb62 100644
--- a/zht/api/presets/model/index.html
+++ b/zht/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼
python
@staticmethod
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

-    
+    
     
   
 
\ No newline at end of file