diff --git a/404.html b/404.html index f74c953..8604d6b 100644 --- a/404.html +++ b/404.html @@ -8,7 +8,7 @@ - + @@ -16,7 +16,7 @@
- + \ No newline at end of file diff --git a/api/index.html b/api/index.html index 29814d2..08b8db1 100644 --- a/api/index.html +++ b/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp

本模块是主模块,提供了一些工具 可导入

mbcp.mp_math:数学工具

mbcp.particle:粒子生成工具

mbcp.presets:预设

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/api/mp_math/angle.html b/api/mp_math/angle.html index 718c146..58d0afc 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ 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 c935d10..ec3de9b 100644 --- a/api/mp_math/const.html +++ b/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp.mp_math.const

本模块定义了一些常用的常量

var PI

  • 说明: 常量 π

  • 默认值: math.pi

var E

  • 说明: 自然对数的底 exp(1)

  • 默认值: math.e

var GOLDEN_RATIO

  • 说明: 黄金分割比

  • 默认值: (1 + math.sqrt(5)) / 2

var GAMMA

  • 说明: 欧拉常数

  • 默认值: 0.5772156649015329

var EPSILON

  • 说明: 精度误差

  • 默认值: 0.0001

var APPROX

  • 说明: 约等于判定误差

  • 默认值: 0.001

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html index dc81e33..98ba985 100644 --- a/api/mp_math/equation.html +++ b/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type') - + \ No newline at end of file diff --git a/api/mp_math/function.html b/api/mp_math/function.html index 596e7da..2e61cd2 100644 --- a/api/mp_math/function.html +++ b/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func - + \ No newline at end of file diff --git a/api/mp_math/index.html b/api/mp_math/index.html index 8c670ab..3aca02e 100644 --- a/api/mp_math/index.html +++ b/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp.mp_math

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

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/api/mp_math/line.html b/api/mp_math/line.html index c59e573..6d64dfc 100644 --- a/api/mp_math/line.html +++ b/api/mp_math/line.html @@ -8,10 +8,10 @@ - - + + - + @@ -22,7 +22,7 @@ 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:

返回: bool: 是否近似相等

源代码在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     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:

返回: AnyAngle: 夹角

源代码在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

说明: 计算直线和直线或点之间的距离。

参数:

返回: float: 距离

引发:

源代码在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

说明: 计算直线和直线或点之间的距离。

TIP

直线和直线之间的距离计算公式:

TIP

直线和点之间的距离计算公式:

|P1P×v||v|

其中,P1为直线上的点,P为点,v为直线的方向向量。

参数:

返回: float: 距离

引发:

源代码在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     if isinstance(other, Line3):
         if self == other:
             return 0
@@ -35,38 +35,38 @@
     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:

返回: Point3: 交点

引发:

源代码在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')

method cal_intersection(self, other: Line3) -> Point3

说明: 计算两条直线的交点。

参数:

返回: Point3: 交点

引发:

源代码在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     if self.is_parallel(other):
         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:

返回: Line3: 垂线

源代码在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

说明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

参数:

返回: Point3: 点

源代码在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
-    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

说明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源代码在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    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:

返回: bool: 是否近似平行

源代码在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

说明: 判断两条直线是否平行。

参数:

返回: bool: 是否平行

源代码在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
-    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

说明: 判断两条直线是否共线。

参数:

返回: bool: 是否共线

源代码在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

说明: 判断点是否在直线上。

参数:

返回: bool: 是否在直线上

源代码在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
-    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

说明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

参数:

返回: bool: 是否共面

源代码在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
-    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

源代码在GitHub上查看
python
def simplify(self):
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3

说明: 计算直线经过指定点p的垂线。

参数:

返回: Line3: 垂线

源代码在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

说明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

参数:

返回: Point3: 点

源代码在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

说明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源代码在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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:

返回: bool: 是否近似平行

源代码在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

说明: 判断两条直线是否平行。

参数:

返回: bool: 是否平行

源代码在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

说明: 判断两条直线是否共线。

参数:

返回: bool: 是否共线

源代码在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

说明: 判断点是否在直线上。

参数:

返回: bool: 是否在直线上

源代码在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
+    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

说明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

参数:

返回: bool: 是否共面

源代码在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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

源代码在GitHub上查看
python
def simplify(self):
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
     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:

返回: Line3: 直线

源代码在GitHub上查看
python
@classmethod
+        self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3

说明: 工厂函数 由两点构造直线。

参数:

返回: Line3: 直线

源代码在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method 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:

返回: Line3 | Point3 | None: 交集

源代码在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method 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:

返回: Line3 | Point3 | None: 交集

源代码在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)

method self == other => bool

说明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

参数:

返回: bool: 是否等价

源代码在GitHub上查看
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)

method self == other => bool

说明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

参数:

返回: bool: 是否等价

源代码在GitHub上查看
python
def __eq__(self, other) -> bool:
     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 f30888b..1f72a93 100644 --- a/api/mp_math/mp_math_typing.html +++ b/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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模块 mbcp.mp_math.mp_math_typing

本模块用于内部类型提示

var RealNumber

  • 说明: 实数

  • 类型: TypeAlias

  • 默认值: int | float

var Number

  • 说明: 数

  • 类型: TypeAlias

  • 默认值: RealNumber | complex

var SingleVar

  • 说明: 单变量

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

var ArrayVar

  • 说明: 数组变量

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

var Var

  • 说明: 变量

  • 类型: TypeAlias

  • 默认值: SingleVar | ArrayVar

var OneSingleVarFunc

  • 说明: 一元单变量函数

  • 类型: TypeAlias

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

var OneArrayFunc

  • 说明: 一元数组函数

  • 类型: TypeAlias

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

var OneVarFunc

  • 说明: 一元函数

  • 类型: TypeAlias

  • 默认值: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc

  • 说明: 二元单变量函数

  • 类型: TypeAlias

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

var TwoArraysFunc

  • 说明: 二元数组函数

  • 类型: TypeAlias

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

var TwoVarsFunc

  • 说明: 二元函数

  • 类型: TypeAlias

  • 默认值: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc

  • 说明: 三元单变量函数

  • 类型: TypeAlias

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

var ThreeArraysFunc

  • 说明: 三元数组函数

  • 类型: TypeAlias

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

var ThreeVarsFunc

  • 说明: 三元函数

  • 类型: TypeAlias

  • 默认值: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc

  • 说明: 多元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[..., SingleVar]

var MultiArraysFunc

  • 说明: 多元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[..., ArrayVar]

var MultiVarsFunc

  • 说明: 多元函数

  • 类型: TypeAlias

  • 默认值: MultiSingleVarsFunc | MultiArraysFunc

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html index 570b862..72b1240 100644 --- a/api/mp_math/plane.html +++ b/api/mp_math/plane.html @@ -8,10 +8,10 @@ - - + + - + @@ -39,13 +39,13 @@ 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:

返回: float: 距离

引发:

源代码在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float

说明: 计算平面与平面或点之间的距离。

TIP

平面和平面之间的距离计算公式: 暂未实现

TIP

平面和点之间的距离计算公式:

|P1Pn||n|

其中,P1为平面上的点,P为点,n为平面的法向量。

参数:

返回: float: 距离

引发:

源代码在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     if isinstance(other, Plane3):
-        return 0
+        raise NotImplementedError('Not implemented yet.')
     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。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点,依次假设x=0, y=0, z=0,并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

xx0m=yy0n=zz0p

参数:

返回: Line3: 交线

引发:

源代码在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3

说明: 计算两平面的交线。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点,依次假设x=0, y=0, z=0,并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

xx0m=yy0n=zz0p

参数:

返回: Line3: 交线

引发:

源代码在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -62,37 +62,37 @@
         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:

返回: Point3: 交点

引发:

源代码在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3

说明: 计算平面与直线的交点。

TIP

计算平面与直线交点的一般步骤:

  1. 求直线的参数方程
  2. 代入平面方程,解出t
  3. 代入直线参数方程,求出交点

参数:

返回: Point3: 交点

引发:

源代码在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     if self.normal @ other.direction == 0:
         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:

返回: Plane3: 平面

源代码在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    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:

返回: bool: 是否平行

源代码在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

说明: 平面的法向量。

返回: Vector3: 法向量

源代码在GitHub上查看
python
@property
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3

说明: 计算平行于该平面且过指定点的平面。

参数:

返回: Plane3: 平面

源代码在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    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:

返回: bool: 是否平行

源代码在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

说明: 平面的法向量。

返回: Vector3: 法向量

源代码在GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

说明: 工厂函数 由点和法向量构造平面(点法式构造)。

参数:

返回: Plane3: 平面

源代码在GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

说明: 工厂函数 由点和法向量构造平面(点法式构造)。

参数:

返回: Plane3: 平面

源代码在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     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:

返回: 平面

源代码在GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3

说明: 工厂函数 由三点构造平面。

参数:

返回: 平面

源代码在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     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:

返回: 平面

源代码在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3

说明: 工厂函数 由两直线构造平面。

参数:

返回: 平面

源代码在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     v1 = l1.direction
     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:

返回: 平面

源代码在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3

说明: 工厂函数 由点和直线构造平面。

参数:

返回: 平面

源代码在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

源代码在GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

源代码在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method self & other: Plane3 => Line3 | None

源代码在GitHub上查看
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None

源代码在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method self & other

说明: 取两平面的交集(人话:交线)

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码在GitHub上查看
python
def __and__(self, other):
+    ...

method self & other

说明: 取两平面的交集(人话:交线)

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码在GitHub上查看
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -102,10 +102,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码在GitHub上查看
python
def __eq__(self, other) -> bool:
-    return self.approx(other)

method self & other: Line3 => Point3

源代码在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码在GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.approx(other)

method self & other: Line3 => Point3

源代码在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
- + \ No newline at end of file diff --git a/api/mp_math/point.html b/api/mp_math/point.html index ded9cec..95d06d6 100644 --- a/api/mp_math/point.html +++ b/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3

说明: P - P -> V

P - V -> P 已在 Vector3 中实现

参数:

返回: Vector3: 新的向量

源代码在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     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 d9a1703..63e3efe 100644 --- a/api/mp_math/segment.html +++ b/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -27,7 +27,7 @@ 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 9f423e1..3967fe0 100644 --- a/api/mp_math/utils.html +++ b/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return '' - + \ No newline at end of file diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html index 72b6f6e..30b42ec 100644 --- a/api/mp_math/vector.html +++ b/api/mp_math/vector.html @@ -8,8 +8,8 @@ - - + + @@ -79,7 +79,7 @@ return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3

源代码在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3

说明: 取负。

返回: Vector3: 负向量

源代码在GitHub上查看
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3

var x_axis

var y_axis

var z_axis

- + \ No newline at end of file diff --git a/api/particle/index.html b/api/particle/index.html index 42c6ccc..67f62e7 100644 --- a/api/particle/index.html +++ b/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

模块 mbcp.particle

本模块定义了粒子生成相关的工具

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/api/presets/index.html b/api/presets/index.html index a9ec96d..d241bee 100644 --- a/api/presets/index.html +++ b/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/api/presets/model/index.html b/api/presets/model/index.html index 0ea47e7..628462d 100644 --- a/api/presets/model/index.html +++ b/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -28,7 +28,7 @@ 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_line.md.BufsPjQ4.js b/assets/api_mp_math_line.md.BufsPjQ4.js deleted file mode 100644 index 804f098..0000000 --- a/assets/api_mp_math_line.md.BufsPjQ4.js +++ /dev/null @@ -1,48 +0,0 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),n={name:"api/mp_math/line.md"},e=t(`

模块 mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

说明: 三维空间中的直线。由一个点和一个方向向量确定。

参数:

源代码在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    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:

返回: bool: 是否近似相等

源代码在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    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:

返回: AnyAngle: 夹角

源代码在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

说明: 计算直线和直线或点之间的距离。

参数:

返回: float: 距离

引发:

源代码在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
-    if isinstance(other, Line3):
-        if self == other:
-            return 0
-        elif self.is_parallel(other):
-            return (other.point - self.point).cross(self.direction).length / self.direction.length
-        elif not self.is_coplanar(other):
-            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
-        else:
-            return 0
-    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:

返回: Point3: 交点

引发:

源代码在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    if self.is_parallel(other):
-        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:

返回: Line3: 垂线

源代码在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

说明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

参数:

返回: Point3: 点

源代码在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
-    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

说明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源代码在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    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:

返回: bool: 是否近似平行

源代码在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

说明: 判断两条直线是否平行。

参数:

返回: bool: 是否平行

源代码在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
-    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

说明: 判断两条直线是否共线。

参数:

返回: bool: 是否共线

源代码在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

说明: 判断点是否在直线上。

参数:

返回: bool: 是否在直线上

源代码在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
-    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

说明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

参数:

返回: bool: 是否共面

源代码在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
-    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

源代码在GitHub上查看
python
def simplify(self):
-    self.direction.normalize()
-    if self.direction.x == 0:
-        self.point.x = 0
-    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:

返回: Line3: 直线

源代码在GitHub上查看
python
@classmethod
-def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    direction = p2 - p1
-    return cls(p1, direction)

method 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:

返回: Line3 | Point3 | None: 交集

源代码在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    if self.is_collinear(other):
-        return self
-    elif self.is_parallel(other) or not self.is_coplanar(other):
-        return None
-    else:
-        return self.cal_intersection(other)

method self == other => bool

说明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

参数:

返回: bool: 是否等价

源代码在GitHub上查看
python
def __eq__(self, other) -> bool:
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/api_mp_math_line.md.BufsPjQ4.lean.js b/assets/api_mp_math_line.md.BufsPjQ4.lean.js deleted file mode 100644 index 528ed79..0000000 --- a/assets/api_mp_math_line.md.BufsPjQ4.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),n={name:"api/mp_math/line.md"},e=t("",106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/api_mp_math_line.md.rTuT8qsY.js b/assets/api_mp_math_line.md.rTuT8qsY.js new file mode 100644 index 0000000..0763347 --- /dev/null +++ b/assets/api_mp_math_line.md.rTuT8qsY.js @@ -0,0 +1,44 @@ +import{_ as n,c as i,j as s,a as t,a4 as e,o as a}from"./chunks/framework.DpC1ZpOZ.js";const rs=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},h=e('

模块 mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

说明: 三维空间中的直线。由一个点和一个方向向量确定。

参数:

源代码在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):\n    self.point = point\n    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:

返回: bool: 是否近似相等

源代码在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:\n    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:

返回: AnyAngle: 夹角

源代码在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':\n    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。

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参数:

返回: float: 距离

引发:

源代码在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    if isinstance(other, Line3):
+        if self == other:
+            return 0
+        elif self.is_parallel(other):
+            return (other.point - self.point).cross(self.direction).length / self.direction.length
+        elif not self.is_coplanar(other):
+            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
+        else:
+            return 0
+    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:

返回: Point3: 交点

引发:

源代码在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+    if self.is_parallel(other):
+        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:

返回: Line3: 垂线

源代码在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

说明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

参数:

返回: Point3: 点

源代码在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

说明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源代码在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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:

返回: bool: 是否近似平行

源代码在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

说明: 判断两条直线是否平行。

参数:

返回: bool: 是否平行

源代码在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

说明: 判断两条直线是否共线。

参数:

返回: bool: 是否共线

源代码在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

说明: 判断点是否在直线上。

参数:

返回: bool: 是否在直线上

源代码在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
+    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

说明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

参数:

返回: bool: 是否共面

源代码在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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

源代码在GitHub上查看
python
def simplify(self):
+    self.direction.normalize()
+    if self.direction.x == 0:
+        self.point.x = 0
+    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:

返回: Line3: 直线

源代码在GitHub上查看
python
@classmethod
+def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
+    direction = p2 - p1
+    return cls(p1, direction)

method 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:

返回: Line3 | Point3 | None: 交集

源代码在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    if self.is_collinear(other):
+        return self
+    elif self.is_parallel(other) or not self.is_coplanar(other):
+        return None
+    else:
+        return self.cal_intersection(other)

method self == other => bool

说明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

参数:

返回: bool: 是否等价

源代码在GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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为平面的法向量,"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点,依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e(",并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default}; diff --git a/assets/api_mp_math_plane.md.BI-yBOVt.js b/assets/api_mp_math_plane.md.BfKkYqeh.js similarity index 56% rename from assets/api_mp_math_plane.md.BI-yBOVt.js rename to assets/api_mp_math_plane.md.BfKkYqeh.js index 6b455f8..d3a01e9 100644 --- a/assets/api_mp_math_plane.md.BI-yBOVt.js +++ b/assets/api_mp_math_plane.md.BfKkYqeh.js @@ -1,4 +1,4 @@ -import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),n={name:"api/mp_math/plane.md"},h=t(`

模块 mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class Plane3

method __init__(self, a: float, b: float, c: float, d: float)

说明: 平面方程:ax + by + cz + d = 0

参数:

源代码在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as l,c as t,j as s,a as e,a4 as i,o as a}from"./chunks/framework.DpC1ZpOZ.js";const D1=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),n={name:"api/mp_math/plane.md"},h=i(`

模块 mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class Plane3

method __init__(self, a: float, b: float, c: float, d: float)

说明: 平面方程:ax + by + cz + d = 0

参数:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     self.a = a
     self.b = b
     self.c = c
@@ -13,19 +13,19 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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。

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参数:

返回: AnyAngle: 夹角

引发:

源代码在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False

method cal_angle(self, other: Line3 | Plane3) -> AnyAngle

说明: 计算平面与平面之间的夹角。

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参数:

返回: AnyAngle: 夹角

引发:

源代码在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     if isinstance(other, Line3):
         return self.normal.cal_angle(other.direction).complementary
     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:

返回: float: 距离

引发:

源代码在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float

说明: 计算平面与平面或点之间的距离。

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参数:

返回: float: 距离

引发:

源代码在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     if isinstance(other, Plane3):
-        return 0
+        raise NotImplementedError('Not implemented yet.')
     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。

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参数:

  • other (Plane3): 另一个平面

返回: Line3: 交线

引发:

源代码在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3

说明: 计算两平面的交线。

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参数:

  • other (Plane3): 另一个平面

返回: Line3: 交线

引发:

源代码在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -42,37 +42,37 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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:

返回: Point3: 交点

引发:

源代码在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3

说明: 计算平面与直线的交点。

TIP

计算平面与直线交点的一般步骤:

  1. 求直线的参数方程
  2. 代入平面方程,解出t
  3. 代入直线参数方程,求出交点

参数:

返回: Point3: 交点

引发:

源代码在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     if self.normal @ other.direction == 0:
         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:

返回: Plane3: 平面

源代码在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

说明: 判断两个平面是否平行。

参数:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源代码在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

说明: 平面的法向量。

返回: Vector3: 法向量

源代码在GitHub上查看
python
@property
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3

说明: 计算平行于该平面且过指定点的平面。

参数:

返回: Plane3: 平面

源代码在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

说明: 判断两个平面是否平行。

参数:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源代码在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

说明: 平面的法向量。

返回: Vector3: 法向量

源代码在GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

说明: 工厂函数 由点和法向量构造平面(点法式构造)。

参数:

返回: Plane3: 平面

源代码在GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

说明: 工厂函数 由点和法向量构造平面(点法式构造)。

参数:

返回: Plane3: 平面

源代码在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     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 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源代码在GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3

说明: 工厂函数 由三点构造平面。

参数:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源代码在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     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 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源代码在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3

说明: 工厂函数 由两直线构造平面。

参数:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源代码在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     v1 = l1.direction
     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:

返回: 平面

源代码在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3

说明: 工厂函数 由点和直线构造平面。

参数:

返回: 平面

源代码在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

源代码在GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

源代码在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method self & other: Plane3 => Line3 | None

源代码在GitHub上查看
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None

源代码在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method self & other

说明: 取两平面的交集(人话:交线)

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码在GitHub上查看
python
def __and__(self, other):
+    ...

method self & other

说明: 取两平面的交集(人话:交线)

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码在GitHub上查看
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -82,6 +82,6 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

说明: 判断两个平面是否等价。

参数:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源代码在GitHub上查看
python
def __eq__(self, other) -> bool:
-    return self.approx(other)

method self & other: Line3 => Point3

源代码在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
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method self == other => bool

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码在GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.approx(other)

method self & other: Line3 => Point3

源代码在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
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mbcp.mp_math.line","class Line3"]},"57":{"title":"method self == other => bool","titles":["Module mbcp.mp_math.line","class Line3"]},"58":{"title":"Module mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["Module mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["Module mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["Module mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"76":{"title":"Module mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["Module mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["Module mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["Module mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["Module mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["Module mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method self == other => bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method self & other: Line3 => Point3","titles":["Module mbcp.mp_math.plane","class 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= False) -> str","titles":["Module mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"118":{"title":"Module mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["Module mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["Module mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method 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ThreeSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"76":{"title":"モジュール mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["モジュール mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> 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CurveEquation"]},"33":{"title":"method self () *t: Var => Point3 | tuple[Point3, ...]","titles":["模块 mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模块 mbcp.mp_math.equation"]},"35":{"title":"模块 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模块 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模块 mbcp.mp_math.function"]},"38":{"title":"模块 mbcp.mp_math","titles":[]},"39":{"title":"模块 mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["模块 mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模块 mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模块 mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模块 mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模块 mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["模块 mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["模块 mbcp.mp_math.line","class Line3"]},"57":{"title":"method self == other => bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"58":{"title":"模块 mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["模块 mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模块 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模块 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"76":{"title":"模块 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模块 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method self == other => bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method self & other: Line3 => Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模块 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模块 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模块 mbcp.mp_math.point","class Point3"]},"103":{"title":"method self == other","titles":["模块 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模块 mbcp.mp_math.point","class Point3"]},"105":{"title":"模块 mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["模块 mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模块 mbcp.mp_math.segment","class Segment3"]},"108":{"title":"模块 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模块 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模块 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method self == other","titles":["模块 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method self != other","titles":["模块 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"118":{"title":"模块 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模块 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method project(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["模块 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CurveEquation"]},"33":{"title":"method self () *t: Var => Point3 | tuple[Point3, ...]","titles":["模块 mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模块 mbcp.mp_math.equation"]},"35":{"title":"模块 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模块 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模块 mbcp.mp_math.function"]},"38":{"title":"模块 mbcp.mp_math","titles":[]},"39":{"title":"模块 mbcp.mp_math.mp_math_typing","titles":[]},"40":{"title":"var RealNumber","titles":["模块 mbcp.mp_math.mp_math_typing"]},"41":{"title":"var Number","titles":["模块 mbcp.mp_math.mp_math_typing"]},"42":{"title":"var SingleVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"43":{"title":"var ArrayVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"44":{"title":"var Var","titles":["模块 mbcp.mp_math.mp_math_typing"]},"45":{"title":"var OneSingleVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"46":{"title":"var OneArrayFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"47":{"title":"var OneVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"48":{"title":"var TwoSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"49":{"title":"var TwoArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"50":{"title":"var TwoVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"51":{"title":"var ThreeSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"52":{"title":"var ThreeArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"53":{"title":"var ThreeVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"54":{"title":"var MultiSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"55":{"title":"var MultiArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"56":{"title":"var MultiVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"57":{"title":"模块 mbcp.mp_math.line","titles":[]},"58":{"title":"class Line3","titles":["模块 mbcp.mp_math.line"]},"59":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模块 mbcp.mp_math.line","class Line3"]},"60":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"61":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模块 mbcp.mp_math.line","class Line3"]},"62":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模块 mbcp.mp_math.line","class Line3"]},"63":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"64":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"65":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"66":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模块 mbcp.mp_math.line","class Line3"]},"67":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"68":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"69":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"70":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"71":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"72":{"title":"method simplify(self)","titles":["模块 mbcp.mp_math.line","class Line3"]},"73":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"74":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["模块 mbcp.mp_math.line","class Line3"]},"75":{"title":"method self == other => bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"76":{"title":"模块 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模块 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method self == other => bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method self & other: Line3 => Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模块 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模块 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模块 mbcp.mp_math.point","class Point3"]},"103":{"title":"method self == other","titles":["模块 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模块 mbcp.mp_math.point","class Point3"]},"105":{"title":"模块 mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["模块 mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模块 mbcp.mp_math.segment","class Segment3"]},"108":{"title":"模块 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模块 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模块 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method self == other","titles":["模块 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method self != other","titles":["模块 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"118":{"title":"模块 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模块 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method project(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - 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CurveEquation"]},"33":{"title":"method self () *t: Var => Point3 | tuple[Point3, ...]","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模組 mbcp.mp_math.equation"]},"35":{"title":"模組 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模組 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模組 mbcp.mp_math.function"]},"38":{"title":"模組 mbcp.mp_math","titles":[]},"39":{"title":"模組 mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["模組 mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模組 mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模組 mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模組 mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模組 mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["模組 mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["模組 mbcp.mp_math.line","class Line3"]},"57":{"title":"method self == other => bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"58":{"title":"模組 mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["模組 mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模組 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模組 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"76":{"title":"模組 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模組 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method self == other => bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method self & other: Line3 => Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模組 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模組 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模組 mbcp.mp_math.point","class Point3"]},"103":{"title":"method self == other","titles":["模組 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模組 mbcp.mp_math.point","class Point3"]},"105":{"title":"模組 mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["模組 mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模組 mbcp.mp_math.segment","class Segment3"]},"108":{"title":"模組 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模組 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模組 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method self == other","titles":["模組 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method self != other","titles":["模組 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"118":{"title":"模組 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模組 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method project(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["模組 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self / other: float => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"模組 mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["模組 mbcp.mp_math.const"]},"25":{"title":"var E","titles":["模組 mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["模組 mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["模組 mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["模組 mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["模組 mbcp.mp_math.const"]},"30":{"title":"模組 mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["模組 mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method self () *t: Var => Point3 | tuple[Point3, ...]","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模組 mbcp.mp_math.equation"]},"35":{"title":"模組 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模組 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模組 mbcp.mp_math.function"]},"38":{"title":"模組 mbcp.mp_math","titles":[]},"39":{"title":"模組 mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["模組 mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模組 mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模組 mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模組 mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模組 mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["模組 mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["模組 mbcp.mp_math.line","class Line3"]},"57":{"title":"method self == other => bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"58":{"title":"模組 mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["模組 mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模組 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模組 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"76":{"title":"模組 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模組 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method self == other => bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method self & other: Line3 => Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模組 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模組 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模組 mbcp.mp_math.point","class Point3"]},"103":{"title":"method self == other","titles":["模組 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模組 mbcp.mp_math.point","class Point3"]},"105":{"title":"模組 mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["模組 mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模組 mbcp.mp_math.segment","class Segment3"]},"108":{"title":"模組 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模組 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模組 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method self == other","titles":["模組 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method self != other","titles":["模組 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"118":{"title":"模組 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模組 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method project(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["模組 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rs=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),l={name:"en/api/mp_math/line.md"},h=e('

Module mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

Description: 三维空间中的直线。由一个点和一个方向向量确定。

Arguments:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):\n    self.point = point\n    self.direction = direction

method approx(self, other: Line3, epsilon: float = APPROX) -> bool

Description: 判断两条直线是否近似相等。

Arguments:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:\n    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

Description: 计算直线和直线之间的夹角。

Arguments:

  • other (Line3): 另一条直线

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':\n    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。

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Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    if isinstance(other, Line3):
+        if self == other:
+            return 0
+        elif self.is_parallel(other):
+            return (other.point - self.point).cross(self.direction).length / self.direction.length
+        elif not self.is_coplanar(other):
+            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
+        else:
+            return 0
+    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 (Line3): 另一条直线

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+    if self.is_parallel(other):
+        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:

Return: Line3: 垂线

Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

Description: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

Arguments:

Return: Point3: 点

Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

Description: 获取直线的参数方程。

Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

Description: 判断两条直线是否近似平行。

Arguments:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

Description: 判断两条直线是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

Description: 判断两条直线是否共线。

Arguments:

Return: bool: 是否共线

Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

Description: 判断点是否在直线上。

Arguments:

Return: bool: 是否在直线上

Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
+    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

Description: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

Arguments:

Return: bool: 是否共面

Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

Description: 简化直线方程,等价相等。 自体简化,不返回值。

按照可行性一次对x y z 化 0 处理,并对向量单位化

Source code or View on GitHub
python
def simplify(self):
+    self.direction.normalize()
+    if self.direction.x == 0:
+        self.point.x = 0
+    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:

Return: Line3: 直线

Source code or View on GitHub
python
@classmethod
+def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
+    direction = p2 - p1
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

Description: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

Arguments:

  • other (Line3): 另一条直线

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    if self.is_collinear(other):
+        return self
+    elif self.is_parallel(other) or not self.is_coplanar(other):
+        return None
+    else:
+        return self.cal_intersection(other)

method self == other => bool

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

  • other (Line3): 另一条直线

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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Module mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

Description: 三维空间中的直线。由一个点和一个方向向量确定。

Arguments:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    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 (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

Description: 计算直线和直线之间的夹角。

Arguments:

  • other (Line3): 另一条直线

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

Description: 计算直线和直线或点之间的距离。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
-    if isinstance(other, Line3):
-        if self == other:
-            return 0
-        elif self.is_parallel(other):
-            return (other.point - self.point).cross(self.direction).length / self.direction.length
-        elif not self.is_coplanar(other):
-            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
-        else:
-            return 0
-    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 (Line3): 另一条直线

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    if self.is_parallel(other):
-        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:

Return: Line3: 垂线

Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

Description: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

Arguments:

Return: Point3: 点

Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
-    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

Description: 获取直线的参数方程。

Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

Description: 判断两条直线是否近似平行。

Arguments:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

Description: 判断两条直线是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
-    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

Description: 判断两条直线是否共线。

Arguments:

Return: bool: 是否共线

Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

Description: 判断点是否在直线上。

Arguments:

Return: bool: 是否在直线上

Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
-    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

Description: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

Arguments:

Return: bool: 是否共面

Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

Description: 简化直线方程,等价相等。 自体简化,不返回值。

按照可行性一次对x y z 化 0 处理,并对向量单位化

Source code or View on GitHub
python
def simplify(self):
-    self.direction.normalize()
-    if self.direction.x == 0:
-        self.point.x = 0
-    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:

Return: Line3: 直线

Source code or View on GitHub
python
@classmethod
-def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    direction = p2 - p1
-    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

Description: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

Arguments:

  • other (Line3): 另一条直线

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    if self.is_collinear(other):
-        return self
-    elif self.is_parallel(other) or not self.is_coplanar(other):
-        return None
-    else:
-        return self.cal_intersection(other)

method self == other => bool

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

  • other (Line3): 另一条直线

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=t(`

Module mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class Plane3

method __init__(self, a: float, b: float, c: float, d: float)

Description: 平面方程:ax + by + cz + d = 0

Arguments:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
Source code or View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as l,c as t,j as s,a as e,a4 as i,o as a}from"./chunks/framework.DpC1ZpOZ.js";const D1=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),n={name:"en/api/mp_math/plane.md"},h=i(`

Module mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class Plane3

method __init__(self, a: float, b: float, c: float, d: float)

Description: 平面方程:ax + by + cz + d = 0

Arguments:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
Source code or View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
     self.a = a
     self.b = b
     self.c = c
@@ -13,19 +13,19 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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。

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Arguments:

Return: AnyAngle: 夹角

Raises:

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False

method cal_angle(self, other: Line3 | Plane3) -> AnyAngle

Description: 计算平面与平面之间的夹角。

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Arguments:

Return: AnyAngle: 夹角

Raises:

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     if isinstance(other, Line3):
         return self.normal.cal_angle(other.direction).complementary
     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:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float

Description: 计算平面与平面或点之间的距离。

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1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mrow",{"data-mjx-texclass":"ORD"},[s("mover",null,[s("mi",null,"n"),s("mo",{stretchy:"false"},"→")])])])],-1),j3=i(`

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     if isinstance(other, Plane3):
-        return 0
+        raise NotImplementedError('Not implemented yet.')
     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。

`,16),I={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 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0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left 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0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t('',1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`

Arguments:

  • other (Plane3): 另一个平面

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3

Description: 计算两平面的交线。

`,8),q3={class:"tip custom-block"},R3=s("p",{class:"custom-block-title"},"TIP",-1),I3=s("p",null,"计算两平面交线的一般步骤:",-1),N3=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),z3={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},G3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},O3=i('',1),J3=[O3],X3=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),$3={start:"2"},U3={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},K3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},W3=i('',1),Y3=[W3],s1=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),t1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},a1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},i1=i('',1),e1=[i1],l1=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),n1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},h1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},o1=i('',1),r1=[o1],p1=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),d1={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Q1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},k1=i('',1),T1=[k1],m1=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left 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0",position:"relative"}},y1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},E1=i('',1),u1=[E1],_1=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),f1=i(`

Arguments:

  • other (Plane3): 另一个平面

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -42,37 +42,37 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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:

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3

Description: 计算平面与直线的交点。

TIP

计算平面与直线交点的一般步骤:

  1. 求直线的参数方程
  2. 代入平面方程,解出t
  3. 代入直线参数方程,求出交点

Arguments:

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     if self.normal @ other.direction == 0:
         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:

Return: Plane3: 平面

Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

Description: 判断两个平面是否平行。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

Description: 平面的法向量。

Return: Vector3: 法向量

Source code or View on GitHub
python
@property
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3

Description: 计算平行于该平面且过指定点的平面。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

Description: 判断两个平面是否平行。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

Description: 平面的法向量。

Return: Vector3: 法向量

Source code or View on GitHub
python
@property
 def normal(self) -> 'Vector3':
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

Description: 工厂函数 由点和法向量构造平面(点法式构造)。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

Description: 工厂函数 由点和法向量构造平面(点法式构造)。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     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 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3

Description: 工厂函数 由三点构造平面。

Arguments:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     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 (Line3): 直线
  • l2 (Line3): 直线

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3

Description: 工厂函数 由两直线构造平面。

Arguments:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     v1 = l1.direction
     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:

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3

Description: 工厂函数 由点和直线构造平面。

Arguments:

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

Source code or View on GitHub
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method self & other: Plane3 => Line3 | None

Source code or View on GitHub
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None

Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method self & other

Description: 取两平面的交集(人话:交线)

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
+    ...

method self & other

Description: 取两平面的交集(人话:交线)

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -82,6 +82,6 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

Description: 判断两个平面是否等价。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
-    return self.approx(other)

method self & other: Line3 => Point3

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
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method self == other => bool

Description: 判断两个平面是否等价。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
+    return self.approx(other)

method self & other: Line3 => Point3

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
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モジュール mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

説明: 三维空间中的直线。由一个点和一个方向向量确定。

引数:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    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 (Line3): 另一条直线
  • epsilon (float): 误差

戻り値: bool: 是否近似相等

ソースコード または GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

説明: 计算直线和直线之间的夹角。

引数:

  • other (Line3): 另一条直线

戻り値: AnyAngle: 夹角

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

説明: 计算直线和直线或点之间的距离。

引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
-    if isinstance(other, Line3):
-        if self == other:
-            return 0
-        elif self.is_parallel(other):
-            return (other.point - self.point).cross(self.direction).length / self.direction.length
-        elif not self.is_coplanar(other):
-            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
-        else:
-            return 0
-    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 (Line3): 另一条直线

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    if self.is_parallel(other):
-        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:

戻り値: Line3: 垂线

ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

説明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

引数:

戻り値: Point3: 点

ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
-    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

説明: 获取直线的参数方程。

戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

説明: 判断两条直线是否近似平行。

引数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

戻り値: bool: 是否近似平行

ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

説明: 判断两条直线是否平行。

引数:

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
-    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

説明: 判断两条直线是否共线。

引数:

戻り値: bool: 是否共线

ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

説明: 判断点是否在直线上。

引数:

戻り値: bool: 是否在直线上

ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
-    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

説明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

引数:

戻り値: bool: 是否共面

ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

説明: 简化直线方程,等价相等。 自体简化,不返回值。

按照可行性一次对x y z 化 0 处理,并对向量单位化

ソースコード または GitHubで表示
python
def simplify(self):
-    self.direction.normalize()
-    if self.direction.x == 0:
-        self.point.x = 0
-    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:

戻り値: Line3: 直线

ソースコード または GitHubで表示
python
@classmethod
-def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    direction = p2 - p1
-    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

説明: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

引数:

  • other (Line3): 另一条直线

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    if self.is_collinear(other):
-        return self
-    elif self.is_parallel(other) or not self.is_coplanar(other):
-        return None
-    else:
-        return self.cal_intersection(other)

method self == other => bool

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

引数:

  • other (Line3): 另一条直线

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/ja_api_mp_math_line.md.ACj3eb2t.lean.js b/assets/ja_api_mp_math_line.md.ACj3eb2t.lean.js deleted file mode 100644 index e30db9d..0000000 --- a/assets/ja_api_mp_math_line.md.ACj3eb2t.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),n={name:"ja/api/mp_math/line.md"},e=t("",106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/ja_api_mp_math_line.md.jOqN-tUX.js b/assets/ja_api_mp_math_line.md.jOqN-tUX.js new file mode 100644 index 0000000..64eb22a --- /dev/null +++ b/assets/ja_api_mp_math_line.md.jOqN-tUX.js @@ -0,0 +1,44 @@ +import{_ as n,c as i,j as s,a as t,a4 as e,o as a}from"./chunks/framework.DpC1ZpOZ.js";const rs=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},h=e('

モジュール mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

説明: 三维空间中的直线。由一个点和一个方向向量确定。

引数:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):\n    self.point = point\n    self.direction = direction

method approx(self, other: Line3, epsilon: float = APPROX) -> bool

説明: 判断两条直线是否近似相等。

引数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

戻り値: bool: 是否近似相等

ソースコード または GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:\n    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

説明: 计算直线和直线之间的夹角。

引数:

  • other (Line3): 另一条直线

戻り値: AnyAngle: 夹角

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':\n    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。

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引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    if isinstance(other, Line3):
+        if self == other:
+            return 0
+        elif self.is_parallel(other):
+            return (other.point - self.point).cross(self.direction).length / self.direction.length
+        elif not self.is_coplanar(other):
+            return abs(self.direction.cross(other.direction) @ (self.point - other.point) / self.direction.cross(other.direction).length)
+        else:
+            return 0
+    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 (Line3): 另一条直线

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+    if self.is_parallel(other):
+        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:

戻り値: Line3: 垂线

ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

説明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

引数:

戻り値: Point3: 点

ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

説明: 获取直线的参数方程。

戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

説明: 判断两条直线是否近似平行。

引数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

戻り値: bool: 是否近似平行

ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

説明: 判断两条直线是否平行。

引数:

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

説明: 判断两条直线是否共线。

引数:

戻り値: bool: 是否共线

ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

説明: 判断点是否在直线上。

引数:

戻り値: bool: 是否在直线上

ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
+    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

説明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

引数:

戻り値: bool: 是否共面

ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

説明: 简化直线方程,等价相等。 自体简化,不返回值。

按照可行性一次对x y z 化 0 处理,并对向量单位化

ソースコード または GitHubで表示
python
def simplify(self):
+    self.direction.normalize()
+    if self.direction.x == 0:
+        self.point.x = 0
+    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:

戻り値: Line3: 直线

ソースコード または GitHubで表示
python
@classmethod
+def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
+    direction = p2 - p1
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

説明: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

引数:

  • other (Line3): 另一条直线

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    if self.is_collinear(other):
+        return self
+    elif self.is_parallel(other) or not self.is_coplanar(other):
+        return None
+    else:
+        return self.cal_intersection(other)

method self == other => bool

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

引数:

  • other (Line3): 另一条直线

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),n={name:"ja/api/mp_math/plane.md"},h=t(`

モジュール mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class Plane3

method __init__(self, a: float, b: float, c: float, d: float)

説明: 平面方程:ax + by + cz + d = 0

引数:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as l,c as t,j as s,a as e,a4 as i,o as a}from"./chunks/framework.DpC1ZpOZ.js";const D1=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),n={name:"ja/api/mp_math/plane.md"},h=i(`

モジュール mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class Plane3

method __init__(self, a: float, b: float, c: float, d: float)

説明: 平面方程:ax + by + cz + d = 0

引数:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
     self.a = a
     self.b = b
     self.c = c
@@ -13,19 +13,19 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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。

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引数:

戻り値: AnyAngle: 夹角

例外:

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False

method cal_angle(self, other: Line3 | Plane3) -> AnyAngle

説明: 计算平面与平面之间的夹角。

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引数:

戻り値: AnyAngle: 夹角

例外:

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     if isinstance(other, Line3):
         return self.normal.cal_angle(other.direction).complementary
     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:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float

説明: 计算平面与平面或点之间的距离。

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引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     if isinstance(other, Plane3):
-        return 0
+        raise NotImplementedError('Not implemented yet.')
     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。

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引数:

  • other (Plane3): 另一个平面

戻り値: Line3: 交线

例外:

ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3

説明: 计算两平面的交线。

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0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),f1=i(`

引数:

  • other (Plane3): 另一个平面

戻り値: Line3: 交线

例外:

ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -42,37 +42,37 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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:

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3

説明: 计算平面与直线的交点。

TIP

计算平面与直线交点的一般步骤:

  1. 求直线的参数方程
  2. 代入平面方程,解出t
  3. 代入直线参数方程,求出交点

引数:

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     if self.normal @ other.direction == 0:
         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:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

説明: 判断两个平面是否平行。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

説明: 平面的法向量。

戻り値: Vector3: 法向量

ソースコード または GitHubで表示
python
@property
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3

説明: 计算平行于该平面且过指定点的平面。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

説明: 判断两个平面是否平行。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

説明: 平面的法向量。

戻り値: Vector3: 法向量

ソースコード または GitHubで表示
python
@property
 def normal(self) -> 'Vector3':
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     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 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3

説明: 工厂函数 由三点构造平面。

引数:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     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 (Line3): 直线
  • l2 (Line3): 直线

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3

説明: 工厂函数 由两直线构造平面。

引数:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     v1 = l1.direction
     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:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3

説明: 工厂函数 由点和直线构造平面。

引数:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

ソースコード または GitHubで表示
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method self & other: Plane3 => Line3 | None

ソースコード または GitHubで表示
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None

ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method self & other

説明: 取两平面的交集(人话:交线)

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
+    ...

method self & other

説明: 取两平面的交集(人话:交线)

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -82,6 +82,6 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
-    return self.approx(other)

method self & other: Line3 => Point3

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量,"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点,依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e(",并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default}; + raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+    return self.approx(other)

method self & other: Line3 => Point3

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,82);function x1(b1,F1,w1,C1,H1,v1){return a(),t("div",null,[h,s("div",o,[p,r,s("mjx-container",d,[(a(),t("svg",Q,T)),m]),s("p",null,[e("其中 "),s("mjx-container",g,[(a(),t("svg",c,E)),u]),e(" 和 "),s("mjx-container",_,[(a(),t("svg",f,b)),F]),e(" 分别为两个平面的法向量")])]),s("div",w,[C,H,s("mjx-container",v,[(a(),t("svg",L,A)),M]),s("p",null,[e("其中 "),s("mjx-container",V,[(a(),t("svg",B,P)),j]),e(" 为平面的法向量,"),s("mjx-container",S,[(a(),t("svg",q,I)),N]),e(" 为直线的方向向量")])]),z,s("div",G,[O,J,s("ul",null,[X,$,s("li",null,[e("不平行 = "),s("mjx-container",U,[(a(),t("svg",K,Y)),s3]),e(" 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模組 mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

説明: 三维空间中的直线。由一个点和一个方向向量确定。

變數説明:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    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 (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似相等

源碼於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

説明: 计算直线和直线之间的夹角。

變數説明:

  • other (Line3): 另一条直线

返回: AnyAngle: 夹角

源碼於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

説明: 计算直线和直线或点之间的距离。

變數説明:

返回: float: 距离

抛出:

源碼於GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+import{_ as n,c as i,j as s,a as t,a4 as e,o as a}from"./chunks/framework.DpC1ZpOZ.js";const rs=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},h=e('

模組 mbcp.mp_math.line

本模块定义了三维空间中的直线类

class Line3

method __init__(self, point: Point3, direction: Vector3)

説明: 三维空间中的直线。由一个点和一个方向向量确定。

變數説明:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):\n    self.point = point\n    self.direction = direction

method approx(self, other: Line3, epsilon: float = APPROX) -> bool

説明: 判断两条直线是否近似相等。

變數説明:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似相等

源碼於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:\n    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

説明: 计算直线和直线之间的夹角。

變數説明:

  • other (Line3): 另一条直线

返回: AnyAngle: 夹角

源碼於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':\n    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。

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變數説明:

返回: float: 距离

抛出:

源碼於GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     if isinstance(other, Line3):
         if self == other:
             return 0
@@ -15,34 +11,34 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.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 (Line3): 另一条直线

返回: Point3: 交点

抛出:

源碼於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')

method cal_intersection(self, other: Line3) -> Point3

説明: 计算两条直线的交点。

變數説明:

  • other (Line3): 另一条直线

返回: Point3: 交点

抛出:

源碼於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     if self.is_parallel(other):
         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:

返回: Line3: 垂线

源碼於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

説明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

變數説明:

返回: Point3: 点

源碼於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
-    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

説明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源碼於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

説明: 判断两条直线是否近似平行。

變數説明:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似平行

源碼於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

説明: 判断两条直线是否平行。

變數説明:

返回: bool: 是否平行

源碼於GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
-    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

説明: 判断两条直线是否共线。

變數説明:

返回: bool: 是否共线

源碼於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

説明: 判断点是否在直线上。

變數説明:

返回: bool: 是否在直线上

源碼於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
-    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

説明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

變數説明:

返回: bool: 是否共面

源碼於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
-    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

源碼於GitHub上查看
python
def simplify(self):
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3

説明: 计算直线经过指定点p的垂线。

變數説明:

返回: Line3: 垂线

源碼於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

説明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

變數説明:

返回: Point3: 点

源碼於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

説明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源碼於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

説明: 判断两条直线是否近似平行。

變數説明:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似平行

源碼於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

説明: 判断两条直线是否平行。

變數説明:

返回: bool: 是否平行

源碼於GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

説明: 判断两条直线是否共线。

變數説明:

返回: bool: 是否共线

源碼於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

説明: 判断点是否在直线上。

變數説明:

返回: bool: 是否在直线上

源碼於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
+    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

説明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

變數説明:

返回: bool: 是否共面

源碼於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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

源碼於GitHub上查看
python
def simplify(self):
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
     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:

返回: Line3: 直线

源碼於GitHub上查看
python
@classmethod
+        self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3

説明: 工厂函数 由两点构造直线。

變數説明:

返回: Line3: 直线

源碼於GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

説明: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

變數説明:

  • other (Line3): 另一条直线

返回: Line3 | Point3 | None: 交集

源碼於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

説明: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

變數説明:

  • other (Line3): 另一条直线

返回: Line3 | Point3 | None: 交集

源碼於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)

method self == other => bool

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

變數説明:

  • other (Line3): 另一条直线

返回: bool: 是否等价

源碼於GitHub上查看
python
def __eq__(self, other) -> bool:
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; + return self.cal_intersection(other)

method self == other => bool

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

變數説明:

  • other (Line3): 另一条直线

返回: bool: 是否等价

源碼於GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,84);function ts(as,es,ns,ls,hs,os){return a(),i("div",null,[h,s("div",o,[p,r,s("ul",null,[k,s("li",null,[t("平行/异面 = "),s("mjx-container",d,[(a(),i("svg",g,m)),y])]),s("li",null,[t("相交 = 0 其中,"),s("mjx-container",E,[(a(),i("svg",Q,T)),b]),t("和"),s("mjx-container",f,[(a(),i("svg",F,C)),x]),t("分别为两条直线上的点,"),s("mjx-container",w,[(a(),i("svg",v,A)),B]),t("为直线的方向向量。")])])]),s("div",L,[H,V,s("mjx-container",P,[(a(),i("svg",q,j)),S]),s("p",null,[t("其中,"),s("mjx-container",Z,[(a(),i("svg",O,G)),N]),t("为直线上的点,"),s("mjx-container",I,[(a(),i("svg",z,J)),$]),t("为点,"),s("mjx-container",U,[(a(),i("svg",K,Y)),ss]),t("为直线的方向向量。")])]),is])}const ks=n(l,[["render",ts]]);export{rs as __pageData,ks as default}; diff --git a/assets/zht_api_mp_math_line.md.BRAzcJ1g.lean.js b/assets/zht_api_mp_math_line.md.BRAzcJ1g.lean.js new file mode 100644 index 0000000..491c680 --- /dev/null +++ b/assets/zht_api_mp_math_line.md.BRAzcJ1g.lean.js @@ -0,0 +1 @@ +import{_ as n,c as i,j as s,a as t,a4 as e,o as 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a/assets/zht_api_mp_math_line.md.CqvSdHr8.lean.js b/assets/zht_api_mp_math_line.md.CqvSdHr8.lean.js deleted file mode 100644 index d282918..0000000 --- a/assets/zht_api_mp_math_line.md.CqvSdHr8.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),n={name:"zht/api/mp_math/line.md"},e=t("",106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/zht_api_mp_math_plane.md.u8cWUecu.js b/assets/zht_api_mp_math_plane.md.CtsXvAxw.js similarity index 56% rename from assets/zht_api_mp_math_plane.md.u8cWUecu.js rename to assets/zht_api_mp_math_plane.md.CtsXvAxw.js index cb6a893..124b055 100644 --- a/assets/zht_api_mp_math_plane.md.u8cWUecu.js +++ b/assets/zht_api_mp_math_plane.md.CtsXvAxw.js @@ -1,4 +1,4 @@ -import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),n={name:"zht/api/mp_math/plane.md"},h=t(`

模組 mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class Plane3

method __init__(self, a: float, b: float, c: float, d: float)

説明: 平面方程:ax + by + cz + d = 0

變數説明:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as l,c as t,j as s,a as e,a4 as i,o as a}from"./chunks/framework.DpC1ZpOZ.js";const D1=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),n={name:"zht/api/mp_math/plane.md"},h=i(`

模組 mbcp.mp_math.plane

本模块定义了三维空间中的平面类

class Plane3

method __init__(self, a: float, b: float, c: float, d: float)

説明: 平面方程:ax + by + cz + d = 0

變數説明:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     self.a = a
     self.b = b
     self.c = c
@@ -13,19 +13,19 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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。

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變數説明:

返回: AnyAngle: 夹角

抛出:

源碼於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False

method cal_angle(self, other: Line3 | Plane3) -> AnyAngle

説明: 计算平面与平面之间的夹角。

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變數説明:

返回: AnyAngle: 夹角

抛出:

源碼於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     if isinstance(other, Line3):
         return self.normal.cal_angle(other.direction).complementary
     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:

返回: float: 距离

抛出:

源碼於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float

説明: 计算平面与平面或点之间的距离。

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變數説明:

返回: float: 距离

抛出:

源碼於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     if isinstance(other, Plane3):
-        return 0
+        raise NotImplementedError('Not implemented yet.')
     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。

`,16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 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0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ns={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left 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0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t('',1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`

變數説明:

  • other (Plane3): 另一个平面

返回: Line3: 交线

抛出:

源碼於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3

説明: 计算两平面的交线。

`,8),q3={class:"tip custom-block"},R3=s("p",{class:"custom-block-title"},"TIP",-1),I3=s("p",null,"计算两平面交线的一般步骤:",-1),N3=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),z3={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},G3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},O3=i('',1),J3=[O3],X3=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),$3={start:"2"},U3={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},K3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},W3=i('',1),Y3=[W3],s1=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),t1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},a1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},i1=i('',1),e1=[i1],l1=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),n1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},h1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},o1=i('',1),p1=[o1],r1=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),d1={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},Q1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},k1=i('',1),T1=[k1],m1=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),g1=s("p",null,"或",-1),c1={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},y1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},E1=i('',1),u1=[E1],_1=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),f1=i(`

變數説明:

  • other (Plane3): 另一个平面

返回: Line3: 交线

抛出:

源碼於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -42,37 +42,37 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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:

返回: Point3: 交点

抛出:

源碼於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3

説明: 计算平面与直线的交点。

TIP

计算平面与直线交点的一般步骤:

  1. 求直线的参数方程
  2. 代入平面方程,解出t
  3. 代入直线参数方程,求出交点

變數説明:

返回: Point3: 交点

抛出:

源碼於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     if self.normal @ other.direction == 0:
         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:

返回: Plane3: 平面

源碼於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

説明: 判断两个平面是否平行。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源碼於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

説明: 平面的法向量。

返回: Vector3: 法向量

源碼於GitHub上查看
python
@property
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3

説明: 计算平行于该平面且过指定点的平面。

變數説明:

返回: Plane3: 平面

源碼於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

説明: 判断两个平面是否平行。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源碼於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

説明: 平面的法向量。

返回: Vector3: 法向量

源碼於GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

變數説明:

返回: Plane3: 平面

源碼於GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

變數説明:

返回: Plane3: 平面

源碼於GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     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 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源碼於GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3

説明: 工厂函数 由三点构造平面。

變數説明:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源碼於GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     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 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源碼於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3

説明: 工厂函数 由两直线构造平面。

變數説明:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源碼於GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     v1 = l1.direction
     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:

返回: 平面

源碼於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3

説明: 工厂函数 由点和直线构造平面。

變數説明:

返回: 平面

源碼於GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

源碼於GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

源碼於GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method self & other: Plane3 => Line3 | None

源碼於GitHub上查看
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None

源碼於GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method self & other

説明: 取两平面的交集(人话:交线)

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼於GitHub上查看
python
def __and__(self, other):
+    ...

method self & other

説明: 取两平面的交集(人话:交线)

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼於GitHub上查看
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -82,6 +82,6 @@ import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼於GitHub上查看
python
def __eq__(self, other) -> bool:
-    return self.approx(other)

method self & other: Line3 => Point3

源碼於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
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method self == other => bool

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼於GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.approx(other)

method self & other: Line3 => Point3

源碼於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,82);function x1(b1,F1,w1,C1,H1,v1){return a(),t("div",null,[h,s("div",o,[p,r,s("mjx-container",d,[(a(),t("svg",Q,T)),m]),s("p",null,[e("其中 "),s("mjx-container",g,[(a(),t("svg",c,E)),u]),e(" 和 "),s("mjx-container",_,[(a(),t("svg",f,b)),F]),e(" 分别为两个平面的法向量")])]),s("div",w,[C,H,s("mjx-container",v,[(a(),t("svg",L,A)),M]),s("p",null,[e("其中 "),s("mjx-container",V,[(a(),t("svg",B,P)),j]),e(" 为平面的法向量,"),s("mjx-container",S,[(a(),t("svg",q,I)),N]),e(" 为直线的方向向量")])]),z,s("div",G,[O,J,s("ul",null,[X,$,s("li",null,[e("不平行 = "),s("mjx-container",U,[(a(),t("svg",K,Y)),s3]),e(" 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为平面的法向量,"),s("mjx-container",S,[(i(),a("svg",j,N)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点,依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e(",并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default}; diff --git a/demo/best-practice.html b/demo/best-practice.html index fbfc974..3a68477 100644 --- a/demo/best-practice.html +++ b/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/demo/index.html b/demo/index.html index 377255e..91e3a68 100644 --- a/demo/index.html +++ b/demo/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/en/api/index.html b/en/api/index.html index 272c7c2..a3d3e94 100644 --- a/en/api/index.html +++ b/en/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

Module mbcp

本模块是主模块,提供了一些工具 可导入

mbcp.mp_math:数学工具

mbcp.particle:粒子生成工具

mbcp.presets:预设

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html index 781cd7a..6f2fae9 100644 --- a/en/api/mp_math/angle.html +++ b/en/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html index 8be7ee6..6257e47 100644 --- a/en/api/mp_math/const.html +++ b/en/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

Module mbcp.mp_math.const

本模块定义了一些常用的常量

var PI

  • Description: 常量 π

  • Default: math.pi

var E

  • Description: 自然对数的底 exp(1)

  • Default: math.e

var GOLDEN_RATIO

  • Description: 黄金分割比

  • Default: (1 + math.sqrt(5)) / 2

var GAMMA

  • Description: 欧拉常数

  • Default: 0.5772156649015329

var EPSILON

  • Description: 精度误差

  • Default: 0.0001

var APPROX

  • Description: 约等于判定误差

  • Default: 0.001

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html index a94b104..d97ccfe 100644 --- a/en/api/mp_math/equation.html +++ b/en/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/function.html b/en/api/mp_math/function.html index 931f2a7..f58ca61 100644 --- a/en/api/mp_math/function.html +++ b/en/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html index b1518b3..4a17503 100644 --- a/en/api/mp_math/index.html +++ b/en/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

Module mbcp.mp_math

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

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html index 566cd3d..ec1c120 100644 --- a/en/api/mp_math/line.html +++ b/en/api/mp_math/line.html @@ -8,10 +8,10 @@ - - + + - + @@ -22,7 +22,7 @@ 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 (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

Description: 计算直线和直线之间的夹角。

Arguments:

  • other (Line3): 另一条直线

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

Description: 计算直线和直线或点之间的距离。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。

TIP

直线和直线之间的距离计算公式:

  • 平行/重合 = 0
  • 平行/异面 = |P1P2×v||v|
  • 相交 = 0 其中,P1P2分别为两条直线上的点,v为直线的方向向量。

TIP

直线和点之间的距离计算公式:

|P1P×v||v|

其中,P1为直线上的点,P为点,v为直线的方向向量。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     if isinstance(other, Line3):
         if self == other:
             return 0
@@ -35,38 +35,38 @@
     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 (Line3): 另一条直线

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')

method cal_intersection(self, other: Line3) -> Point3

Description: 计算两条直线的交点。

Arguments:

  • other (Line3): 另一条直线

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     if self.is_parallel(other):
         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:

Return: Line3: 垂线

Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

Description: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

Arguments:

Return: Point3: 点

Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
-    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

Description: 获取直线的参数方程。

Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

Description: 判断两条直线是否近似平行。

Arguments:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

Description: 判断两条直线是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
-    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

Description: 判断两条直线是否共线。

Arguments:

Return: bool: 是否共线

Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

Description: 判断点是否在直线上。

Arguments:

Return: bool: 是否在直线上

Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
-    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

Description: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

Arguments:

Return: bool: 是否共面

Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

Description: 简化直线方程,等价相等。 自体简化,不返回值。

按照可行性一次对x y z 化 0 处理,并对向量单位化

Source code or View on GitHub
python
def simplify(self):
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3

Description: 计算直线经过指定点p的垂线。

Arguments:

Return: Line3: 垂线

Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

Description: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

Arguments:

Return: Point3: 点

Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

Description: 获取直线的参数方程。

Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

Description: 判断两条直线是否近似平行。

Arguments:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

Description: 判断两条直线是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

Description: 判断两条直线是否共线。

Arguments:

Return: bool: 是否共线

Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

Description: 判断点是否在直线上。

Arguments:

Return: bool: 是否在直线上

Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
+    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

Description: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

Arguments:

Return: bool: 是否共面

Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

Description: 简化直线方程,等价相等。 自体简化,不返回值。

按照可行性一次对x y z 化 0 处理,并对向量单位化

Source code or View on GitHub
python
def simplify(self):
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
     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:

Return: Line3: 直线

Source code or View on GitHub
python
@classmethod
+        self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3

Description: 工厂函数 由两点构造直线。

Arguments:

Return: Line3: 直线

Source code or View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

Description: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

Arguments:

  • other (Line3): 另一条直线

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

Description: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

Arguments:

  • other (Line3): 另一条直线

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)

method self == other => bool

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

  • other (Line3): 另一条直线

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)

method self == other => bool

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

  • other (Line3): 另一条直线

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/mp_math_typing.html b/en/api/mp_math/mp_math_typing.html index 9b8ddb7..cd04887 100644 --- a/en/api/mp_math/mp_math_typing.html +++ b/en/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

Module mbcp.mp_math.mp_math_typing

本模块用于内部类型提示

var RealNumber

  • Description: 实数

  • Type: TypeAlias

  • Default: int | float

var Number

  • Description: 数

  • Type: TypeAlias

  • Default: RealNumber | complex

var SingleVar

  • Description: 单变量

  • Default: TypeVar('SingleVar', bound=Number)

var ArrayVar

  • Description: 数组变量

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

var Var

  • Description: 变量

  • Type: TypeAlias

  • Default: SingleVar | ArrayVar

var OneSingleVarFunc

  • Description: 一元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar], SingleVar]

var OneArrayFunc

  • Description: 一元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar], ArrayVar]

var OneVarFunc

  • Description: 一元函数

  • Type: TypeAlias

  • Default: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc

  • Description: 二元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc

  • Description: 二元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc

  • Description: 二元函数

  • Type: TypeAlias

  • Default: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc

  • Description: 三元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc

  • Description: 三元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc

  • Description: 三元函数

  • Type: TypeAlias

  • Default: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc

  • Description: 多元单变量函数

  • Type: TypeAlias

  • Default: Callable[..., SingleVar]

var MultiArraysFunc

  • Description: 多元数组函数

  • Type: TypeAlias

  • Default: Callable[..., ArrayVar]

var MultiVarsFunc

  • Description: 多元函数

  • Type: TypeAlias

  • Default: MultiSingleVarsFunc | MultiArraysFunc

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html index 9db5190..2aa84db 100644 --- a/en/api/mp_math/plane.html +++ b/en/api/mp_math/plane.html @@ -8,10 +8,10 @@ - - + + - + @@ -39,13 +39,13 @@ 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:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float

Description: 计算平面与平面或点之间的距离。

TIP

平面和平面之间的距离计算公式: 暂未实现

  • 平行 = 0
  • 相交 = 0
  • 不平行 = |P1P2n||n| 其中,P1P2分别为两个平面上的点,n为平面的法向量。

TIP

平面和点之间的距离计算公式:

|P1Pn||n|

其中,P1为平面上的点,P为点,n为平面的法向量。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     if isinstance(other, Plane3):
-        return 0
+        raise NotImplementedError('Not implemented yet.')
     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。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点,依次假设x=0, y=0, z=0,并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

xx0m=yy0n=zz0p

Arguments:

  • other (Plane3): 另一个平面

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3

Description: 计算两平面的交线。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点,依次假设x=0, y=0, z=0,并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

xx0m=yy0n=zz0p

Arguments:

  • other (Plane3): 另一个平面

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -62,37 +62,37 @@
         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:

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3

Description: 计算平面与直线的交点。

TIP

计算平面与直线交点的一般步骤:

  1. 求直线的参数方程
  2. 代入平面方程,解出t
  3. 代入直线参数方程,求出交点

Arguments:

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     if self.normal @ other.direction == 0:
         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:

Return: Plane3: 平面

Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

Description: 判断两个平面是否平行。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

Description: 平面的法向量。

Return: Vector3: 法向量

Source code or View on GitHub
python
@property
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3

Description: 计算平行于该平面且过指定点的平面。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

Description: 判断两个平面是否平行。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

Description: 平面的法向量。

Return: Vector3: 法向量

Source code or View on GitHub
python
@property
 def normal(self) -> 'Vector3':
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

Description: 工厂函数 由点和法向量构造平面(点法式构造)。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

Description: 工厂函数 由点和法向量构造平面(点法式构造)。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     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 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3

Description: 工厂函数 由三点构造平面。

Arguments:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     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 (Line3): 直线
  • l2 (Line3): 直线

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3

Description: 工厂函数 由两直线构造平面。

Arguments:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     v1 = l1.direction
     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:

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3

Description: 工厂函数 由点和直线构造平面。

Arguments:

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

Source code or View on GitHub
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method self & other: Plane3 => Line3 | None

Source code or View on GitHub
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None

Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method self & other

Description: 取两平面的交集(人话:交线)

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
+    ...

method self & other

Description: 取两平面的交集(人话:交线)

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -102,10 +102,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

Description: 判断两个平面是否等价。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
-    return self.approx(other)

method self & other: Line3 => Point3

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

Description: 判断两个平面是否等价。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
+    return self.approx(other)

method self & other: Line3 => Point3

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html index 9ebb2b2..65ce717 100644 --- a/en/api/mp_math/point.html +++ b/en/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3

Description: P - P -> V

P - V -> P 已在 Vector3 中实现

Arguments:

Return: Vector3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/segment.html b/en/api/mp_math/segment.html index 57f91e2..23bb79b 100644 --- a/en/api/mp_math/segment.html +++ b/en/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html index 265f578..e5aa79f 100644 --- a/en/api/mp_math/utils.html +++ b/en/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/mp_math/vector.html b/en/api/mp_math/vector.html index 5cd75e3..9579fe1 100644 --- a/en/api/mp_math/vector.html +++ b/en/api/mp_math/vector.html @@ -8,8 +8,8 @@ - - + + @@ -79,7 +79,7 @@ return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3

Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3

Description: 取负。

Return: Vector3: 负向量

Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3

  • Description: 零向量

  • Type: Vector3

  • Default: Vector3(0, 0, 0)

var x_axis

  • Description: x轴单位向量

  • Type: Vector3

  • Default: Vector3(1, 0, 0)

var y_axis

  • Description: y轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 1, 0)

var z_axis

  • Description: z轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 0, 1)

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/api/particle/index.html b/en/api/particle/index.html index 2667563..a10c923 100644 --- a/en/api/particle/index.html +++ b/en/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/api/presets/index.html b/en/api/presets/index.html index 6bf607a..b1c5946 100644 --- a/en/api/presets/index.html +++ b/en/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html index 927b520..d4ac004 100644 --- a/en/api/presets/model/index.html +++ b/en/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/demo/best-practice.html b/en/demo/best-practice.html index 7f95cf4..1f89cc4 100644 --- a/en/demo/best-practice.html +++ b/en/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/guide/index.html b/en/guide/index.html index e1bd0f7..5e12c93 100644 --- a/en/guide/index.html +++ b/en/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

开始不了一点

12x111

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/index.html b/en/index.html index 2ac1a0d..557ce71 100644 --- a/en/index.html +++ b/en/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

MBCP

More basic change particle

A Library for Python to create Minecraft particle effects and geometric figures

MBCP logo

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/en/refer/index.html b/en/refer/index.html index 900a7a9..8ffaac8 100644 --- a/en/refer/index.html +++ b/en/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

Reference

help us to improve the documentation

Documentation built with VitePress | API references generated by litedoc

- + \ No newline at end of file diff --git a/guide/index.html b/guide/index.html index a14b4e5..e2b0c6e 100644 --- a/guide/index.html +++ b/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

快速开始

TIP

建议:把你项目所使用的Python换成PyPy,这样可以提高性能(兼容性优先)

安装

shell
pip install mbcp

文档由 VitePress 构建 | API引用由 litedoc 生成

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diff --git a/index.html b/index.html index d31ccf8..967d7b9 100644 --- a/index.html +++ b/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

MBCP

更多基础变换粒子

用于几何运算和Minecraft粒子制作的库

MBCP logo

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/ja/api/index.html b/ja/api/index.html index bb2428f..8d1c5cf 100644 --- a/ja/api/index.html +++ b/ja/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

モジュール mbcp

本模块是主模块,提供了一些工具 可导入

mbcp.mp_math:数学工具

mbcp.particle:粒子生成工具

mbcp.presets:预设

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/angle.html b/ja/api/mp_math/angle.html index 00bc318..b63a1eb 100644 --- a/ja/api/mp_math/angle.html +++ b/ja/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/const.html b/ja/api/mp_math/const.html index ae21848..1a22114 100644 --- a/ja/api/mp_math/const.html +++ b/ja/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

モジュール mbcp.mp_math.const

本模块定义了一些常用的常量

var PI

  • 説明: 常量 π

  • デフォルト: math.pi

var E

  • 説明: 自然对数的底 exp(1)

  • デフォルト: math.e

var GOLDEN_RATIO

  • 説明: 黄金分割比

  • デフォルト: (1 + math.sqrt(5)) / 2

var GAMMA

  • 説明: 欧拉常数

  • デフォルト: 0.5772156649015329

var EPSILON

  • 説明: 精度误差

  • デフォルト: 0.0001

var APPROX

  • 説明: 约等于判定误差

  • デフォルト: 0.001

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html index f7ff8ca..cf1153b 100644 --- a/ja/api/mp_math/equation.html +++ b/ja/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/function.html b/ja/api/mp_math/function.html index c6c4fec..49d3042 100644 --- a/ja/api/mp_math/function.html +++ b/ja/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/index.html b/ja/api/mp_math/index.html index ea15bef..1c442ce 100644 --- a/ja/api/mp_math/index.html +++ b/ja/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

モジュール mbcp.mp_math

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

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html index 176a80a..54b1d04 100644 --- a/ja/api/mp_math/line.html +++ b/ja/api/mp_math/line.html @@ -8,10 +8,10 @@ - - + + - + @@ -22,7 +22,7 @@ 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 (Line3): 另一条直线
  • epsilon (float): 误差

戻り値: bool: 是否近似相等

ソースコード または GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

説明: 计算直线和直线之间的夹角。

引数:

  • other (Line3): 另一条直线

戻り値: AnyAngle: 夹角

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

説明: 计算直线和直线或点之间的距离。

引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。

TIP

直线和直线之间的距离计算公式:

  • 平行/重合 = 0
  • 平行/异面 = |P1P2×v||v|
  • 相交 = 0 其中,P1P2分别为两条直线上的点,v为直线的方向向量。

TIP

直线和点之间的距离计算公式:

|P1P×v||v|

其中,P1为直线上的点,P为点,v为直线的方向向量。

引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     if isinstance(other, Line3):
         if self == other:
             return 0
@@ -35,38 +35,38 @@
     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 (Line3): 另一条直线

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')

method cal_intersection(self, other: Line3) -> Point3

説明: 计算两条直线的交点。

引数:

  • other (Line3): 另一条直线

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     if self.is_parallel(other):
         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:

戻り値: Line3: 垂线

ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

説明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

引数:

戻り値: Point3: 点

ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
-    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

説明: 获取直线的参数方程。

戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

説明: 判断两条直线是否近似平行。

引数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

戻り値: bool: 是否近似平行

ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

説明: 判断两条直线是否平行。

引数:

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
-    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

説明: 判断两条直线是否共线。

引数:

戻り値: bool: 是否共线

ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

説明: 判断点是否在直线上。

引数:

戻り値: bool: 是否在直线上

ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
-    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

説明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

引数:

戻り値: bool: 是否共面

ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

説明: 简化直线方程,等价相等。 自体简化,不返回值。

按照可行性一次对x y z 化 0 处理,并对向量单位化

ソースコード または GitHubで表示
python
def simplify(self):
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3

説明: 计算直线经过指定点p的垂线。

引数:

戻り値: Line3: 垂线

ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

説明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

引数:

戻り値: Point3: 点

ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

説明: 获取直线的参数方程。

戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

説明: 判断两条直线是否近似平行。

引数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

戻り値: bool: 是否近似平行

ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

説明: 判断两条直线是否平行。

引数:

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

説明: 判断两条直线是否共线。

引数:

戻り値: bool: 是否共线

ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

説明: 判断点是否在直线上。

引数:

戻り値: bool: 是否在直线上

ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
+    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

説明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

引数:

戻り値: bool: 是否共面

ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self)

説明: 简化直线方程,等价相等。 自体简化,不返回值。

按照可行性一次对x y z 化 0 处理,并对向量单位化

ソースコード または GitHubで表示
python
def simplify(self):
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
     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:

戻り値: Line3: 直线

ソースコード または GitHubで表示
python
@classmethod
+        self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3

説明: 工厂函数 由两点构造直线。

引数:

戻り値: Line3: 直线

ソースコード または GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

説明: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

引数:

  • other (Line3): 另一条直线

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

説明: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

引数:

  • other (Line3): 另一条直线

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)

method self == other => bool

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

引数:

  • other (Line3): 另一条直线

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)

method self == other => bool

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

引数:

  • other (Line3): 另一条直线

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ 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 b49a50f..1a97e8f 100644 --- a/ja/api/mp_math/mp_math_typing.html +++ b/ja/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

モジュール mbcp.mp_math.mp_math_typing

本模块用于内部类型提示

var RealNumber

  • 説明: 实数

  • タイプ: TypeAlias

  • デフォルト: int | float

var Number

  • 説明: 数

  • タイプ: TypeAlias

  • デフォルト: RealNumber | complex

var SingleVar

  • 説明: 单变量

  • デフォルト: TypeVar('SingleVar', bound=Number)

var ArrayVar

  • 説明: 数组变量

  • デフォルト: TypeVar('ArrayVar', bound=Iterable[Number])

var Var

  • 説明: 变量

  • タイプ: TypeAlias

  • デフォルト: SingleVar | ArrayVar

var OneSingleVarFunc

  • 説明: 一元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar], SingleVar]

var OneArrayFunc

  • 説明: 一元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar], ArrayVar]

var OneVarFunc

  • 説明: 一元函数

  • タイプ: TypeAlias

  • デフォルト: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc

  • 説明: 二元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc

  • 説明: 二元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc

  • 説明: 二元函数

  • タイプ: TypeAlias

  • デフォルト: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc

  • 説明: 三元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc

  • 説明: 三元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc

  • 説明: 三元函数

  • タイプ: TypeAlias

  • デフォルト: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc

  • 説明: 多元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[..., SingleVar]

var MultiArraysFunc

  • 説明: 多元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[..., ArrayVar]

var MultiVarsFunc

  • 説明: 多元函数

  • タイプ: TypeAlias

  • デフォルト: MultiSingleVarsFunc | MultiArraysFunc

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html index eb93964..c400a47 100644 --- a/ja/api/mp_math/plane.html +++ b/ja/api/mp_math/plane.html @@ -8,10 +8,10 @@ - - + + - + @@ -39,13 +39,13 @@ 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:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float

説明: 计算平面与平面或点之间的距离。

TIP

平面和平面之间的距离计算公式: 暂未实现

  • 平行 = 0
  • 相交 = 0
  • 不平行 = |P1P2n||n| 其中,P1P2分别为两个平面上的点,n为平面的法向量。

TIP

平面和点之间的距离计算公式:

|P1Pn||n|

其中,P1为平面上的点,P为点,n为平面的法向量。

引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     if isinstance(other, Plane3):
-        return 0
+        raise NotImplementedError('Not implemented yet.')
     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。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点,依次假设x=0, y=0, z=0,并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

xx0m=yy0n=zz0p

引数:

  • other (Plane3): 另一个平面

戻り値: Line3: 交线

例外:

ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3

説明: 计算两平面的交线。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点,依次假设x=0, y=0, z=0,并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

xx0m=yy0n=zz0p

引数:

  • other (Plane3): 另一个平面

戻り値: Line3: 交线

例外:

ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -62,37 +62,37 @@
         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:

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3

説明: 计算平面与直线的交点。

TIP

计算平面与直线交点的一般步骤:

  1. 求直线的参数方程
  2. 代入平面方程,解出t
  3. 代入直线参数方程,求出交点

引数:

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     if self.normal @ other.direction == 0:
         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:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

説明: 判断两个平面是否平行。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

説明: 平面的法向量。

戻り値: Vector3: 法向量

ソースコード または GitHubで表示
python
@property
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3

説明: 计算平行于该平面且过指定点的平面。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

説明: 判断两个平面是否平行。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

説明: 平面的法向量。

戻り値: Vector3: 法向量

ソースコード または GitHubで表示
python
@property
 def normal(self) -> 'Vector3':
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     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 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3

説明: 工厂函数 由三点构造平面。

引数:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     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 (Line3): 直线
  • l2 (Line3): 直线

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3

説明: 工厂函数 由两直线构造平面。

引数:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     v1 = l1.direction
     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:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3

説明: 工厂函数 由点和直线构造平面。

引数:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

ソースコード または GitHubで表示
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method self & other: Plane3 => Line3 | None

ソースコード または GitHubで表示
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None

ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method self & other

説明: 取两平面的交集(人话:交线)

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
+    ...

method self & other

説明: 取两平面的交集(人话:交线)

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -102,10 +102,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
-    return self.approx(other)

method self & other: Line3 => Point3

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+    return self.approx(other)

method self & other: Line3 => Point3

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/point.html b/ja/api/mp_math/point.html index 809a0af..0417d99 100644 --- a/ja/api/mp_math/point.html +++ b/ja/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

引数:

戻り値: Vector3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html index a847af1..6ead971 100644 --- a/ja/api/mp_math/segment.html +++ b/ja/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html index e260ba5..2bdf293 100644 --- a/ja/api/mp_math/utils.html +++ b/ja/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html index 7e88e55..16d12f9 100644 --- a/ja/api/mp_math/vector.html +++ b/ja/api/mp_math/vector.html @@ -8,8 +8,8 @@ - - + + @@ -79,7 +79,7 @@ return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3

ソースコード または GitHubで表示
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3

説明: 取负。

戻り値: Vector3: 负向量

ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3

  • 説明: 零向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 0)

var x_axis

  • 説明: x轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(1, 0, 0)

var y_axis

  • 説明: y轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 1, 0)

var z_axis

  • 説明: z轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 1)

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html index 40cd1e7..6ac976f 100644 --- a/ja/api/particle/index.html +++ b/ja/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html index aed80e6..e4f8fdd 100644 --- a/ja/api/presets/index.html +++ b/ja/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html index e2ebb14..151510e 100644 --- a/ja/api/presets/model/index.html +++ b/ja/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/demo/best-practice.html b/ja/demo/best-practice.html index be81b05..20b6a2a 100644 --- a/ja/demo/best-practice.html +++ b/ja/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/guide/index.html b/ja/guide/index.html index ed903d8..b3937d1 100644 --- a/ja/guide/index.html +++ b/ja/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

开始不了一点

12x111

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/index.html b/ja/index.html index 85c8f56..62b59ba 100644 --- a/ja/index.html +++ b/ja/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

MBCP

More basic change particle

ジオメトリ演算とパーティクル作成のためのライブラリ

MBCP logo

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/ja/refer/index.html b/ja/refer/index.html index 4dfa5fd..bc6fd4f 100644 --- a/ja/refer/index.html +++ b/ja/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

Reference

Help us to improve the documentation

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

- + \ No newline at end of file diff --git a/refer/7-differential-euqtion/index.html b/refer/7-differential-euqtion/index.html index ac49686..e0e5143 100644 --- a/refer/7-differential-euqtion/index.html +++ b/refer/7-differential-euqtion/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

微分方程

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/refer/function/curry.html b/refer/function/curry.html index 418569b..7be60fe 100644 --- a/refer/function/curry.html +++ b/refer/function/curry.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/refer/function/function.html b/refer/function/function.html index d86c8d1..57f3a8d 100644 --- a/refer/function/function.html +++ b/refer/function/function.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/refer/index.html b/refer/index.html index ca1fc1b..a5c0efa 100644 --- a/refer/index.html +++ b/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

Reference

Help us to improve the documentation

文档由 VitePress 构建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/index.html b/zht/api/index.html index 105cb74..069db82 100644 --- a/zht/api/index.html +++ b/zht/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

模組 mbcp

本模块是主模块,提供了一些工具 可导入

mbcp.mp_math:数学工具

mbcp.particle:粒子生成工具

mbcp.presets:预设

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/angle.html b/zht/api/mp_math/angle.html index 4cdf0a3..f3eaefb 100644 --- a/zht/api/mp_math/angle.html +++ b/zht/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/const.html b/zht/api/mp_math/const.html index 3322bcc..51d475c 100644 --- a/zht/api/mp_math/const.html +++ b/zht/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

模組 mbcp.mp_math.const

本模块定义了一些常用的常量

var PI

  • 説明: 常量 π

  • 默認值: math.pi

var E

  • 説明: 自然对数的底 exp(1)

  • 默認值: math.e

var GOLDEN_RATIO

  • 説明: 黄金分割比

  • 默認值: (1 + math.sqrt(5)) / 2

var GAMMA

  • 説明: 欧拉常数

  • 默認值: 0.5772156649015329

var EPSILON

  • 説明: 精度误差

  • 默認值: 0.0001

var APPROX

  • 説明: 约等于判定误差

  • 默認值: 0.001

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/equation.html b/zht/api/mp_math/equation.html index e62593e..85f0f12 100644 --- a/zht/api/mp_math/equation.html +++ b/zht/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/function.html b/zht/api/mp_math/function.html index 1cf6048..477f548 100644 --- a/zht/api/mp_math/function.html +++ b/zht/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/index.html b/zht/api/mp_math/index.html index 47d26ea..40cb693 100644 --- a/zht/api/mp_math/index.html +++ b/zht/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

模組 mbcp.mp_math

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

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/line.html b/zht/api/mp_math/line.html index 426abf9..bac197c 100644 --- a/zht/api/mp_math/line.html +++ b/zht/api/mp_math/line.html @@ -8,10 +8,10 @@ - - + + - + @@ -22,7 +22,7 @@ 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 (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似相等

源碼於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

method cal_angle(self, other: Line3) -> AnyAngle

説明: 计算直线和直线之间的夹角。

變數説明:

  • other (Line3): 另一条直线

返回: AnyAngle: 夹角

源碼於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

説明: 计算直线和直线或点之间的距离。

變數説明:

返回: float: 距离

抛出:

源碼於GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float

説明: 计算直线和直线或点之间的距离。

TIP

直线和直线之间的距离计算公式:

  • 平行/重合 = 0
  • 平行/异面 = |P1P2×v||v|
  • 相交 = 0 其中,P1P2分别为两条直线上的点,v为直线的方向向量。

TIP

直线和点之间的距离计算公式:

|P1P×v||v|

其中,P1为直线上的点,P为点,v为直线的方向向量。

變數説明:

返回: float: 距离

抛出:

源碼於GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     if isinstance(other, Line3):
         if self == other:
             return 0
@@ -35,38 +35,38 @@
     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 (Line3): 另一条直线

返回: Point3: 交点

抛出:

源碼於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')

method cal_intersection(self, other: Line3) -> Point3

説明: 计算两条直线的交点。

變數説明:

  • other (Line3): 另一条直线

返回: Point3: 交点

抛出:

源碼於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     if self.is_parallel(other):
         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:

返回: Line3: 垂线

源碼於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

説明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

變數説明:

返回: Point3: 点

源碼於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
-    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

説明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源碼於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

説明: 判断两条直线是否近似平行。

變數説明:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似平行

源碼於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

説明: 判断两条直线是否平行。

變數説明:

返回: bool: 是否平行

源碼於GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
-    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

説明: 判断两条直线是否共线。

變數説明:

返回: bool: 是否共线

源碼於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

説明: 判断点是否在直线上。

變數説明:

返回: bool: 是否在直线上

源碼於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
-    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

説明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

變數説明:

返回: bool: 是否共面

源碼於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
-    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

源碼於GitHub上查看
python
def simplify(self):
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3

説明: 计算直线经过指定点p的垂线。

變數説明:

返回: Line3: 垂线

源碼於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3

説明: 获取直线上的点。同一条直线,但起始点和方向向量不同,则同一个t对应的点不同。

變數説明:

返回: Point3: 点

源碼於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]

説明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源碼於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool

説明: 判断两条直线是否近似平行。

變數説明:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似平行

源碼於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool

説明: 判断两条直线是否平行。

變數説明:

返回: bool: 是否平行

源碼於GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool

説明: 判断两条直线是否共线。

變數説明:

返回: bool: 是否共线

源碼於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool

説明: 判断点是否在直线上。

變數説明:

返回: bool: 是否在直线上

源碼於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
+    return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool

説明: 判断两条直线是否共面。 充要条件:两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

變數説明:

返回: bool: 是否共面

源碼於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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

源碼於GitHub上查看
python
def simplify(self):
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
     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:

返回: Line3: 直线

源碼於GitHub上查看
python
@classmethod
+        self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3

説明: 工厂函数 由两点构造直线。

變數説明:

返回: Line3: 直线

源碼於GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

説明: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

變數説明:

  • other (Line3): 另一条直线

返回: Line3 | Point3 | None: 交集

源碼於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None

説明: 计算两条直线点集合的交集。重合线返回自身,平行线返回None,交线返回交点。

變數説明:

  • other (Line3): 另一条直线

返回: Line3 | Point3 | None: 交集

源碼於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)

method self == other => bool

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

變數説明:

  • other (Line3): 另一条直线

返回: bool: 是否等价

源碼於GitHub上查看
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)

method self == other => bool

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

變數説明:

  • other (Line3): 另一条直线

返回: bool: 是否等价

源碼於GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ 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 c6360ce..930a415 100644 --- a/zht/api/mp_math/mp_math_typing.html +++ b/zht/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

模組 mbcp.mp_math.mp_math_typing

本模块用于内部类型提示

var RealNumber

  • 説明: 实数

  • 類型: TypeAlias

  • 默認值: int | float

var Number

  • 説明: 数

  • 類型: TypeAlias

  • 默認值: RealNumber | complex

var SingleVar

  • 説明: 单变量

  • 默認值: TypeVar('SingleVar', bound=Number)

var ArrayVar

  • 説明: 数组变量

  • 默認值: TypeVar('ArrayVar', bound=Iterable[Number])

var Var

  • 説明: 变量

  • 類型: TypeAlias

  • 默認值: SingleVar | ArrayVar

var OneSingleVarFunc

  • 説明: 一元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar], SingleVar]

var OneArrayFunc

  • 説明: 一元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar], ArrayVar]

var OneVarFunc

  • 説明: 一元函数

  • 類型: TypeAlias

  • 默認值: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc

  • 説明: 二元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc

  • 説明: 二元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc

  • 説明: 二元函数

  • 類型: TypeAlias

  • 默認值: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc

  • 説明: 三元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc

  • 説明: 三元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc

  • 説明: 三元函数

  • 類型: TypeAlias

  • 默認值: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc

  • 説明: 多元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[..., SingleVar]

var MultiArraysFunc

  • 説明: 多元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[..., ArrayVar]

var MultiVarsFunc

  • 説明: 多元函数

  • 類型: TypeAlias

  • 默認值: MultiSingleVarsFunc | MultiArraysFunc

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/plane.html b/zht/api/mp_math/plane.html index 19208f0..79cddb3 100644 --- a/zht/api/mp_math/plane.html +++ b/zht/api/mp_math/plane.html @@ -8,10 +8,10 @@ - - + + - + @@ -39,13 +39,13 @@ 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:

返回: float: 距离

抛出:

源碼於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float

説明: 计算平面与平面或点之间的距离。

TIP

平面和平面之间的距离计算公式: 暂未实现

  • 平行 = 0
  • 相交 = 0
  • 不平行 = |P1P2n||n| 其中,P1P2分别为两个平面上的点,n为平面的法向量。

TIP

平面和点之间的距离计算公式:

|P1Pn||n|

其中,P1为平面上的点,P为点,n为平面的法向量。

變數説明:

返回: float: 距离

抛出:

源碼於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     if isinstance(other, Plane3):
-        return 0
+        raise NotImplementedError('Not implemented yet.')
     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。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点,依次假设x=0, y=0, z=0,并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

xx0m=yy0n=zz0p

變數説明:

  • other (Plane3): 另一个平面

返回: Line3: 交线

抛出:

源碼於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3

説明: 计算两平面的交线。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点,依次假设x=0, y=0, z=0,并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

xx0m=yy0n=zz0p

變數説明:

  • other (Plane3): 另一个平面

返回: Line3: 交线

抛出:

源碼於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -62,37 +62,37 @@
         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:

返回: Point3: 交点

抛出:

源碼於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3

説明: 计算平面与直线的交点。

TIP

计算平面与直线交点的一般步骤:

  1. 求直线的参数方程
  2. 代入平面方程,解出t
  3. 代入直线参数方程,求出交点

變數説明:

返回: Point3: 交点

抛出:

源碼於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     if self.normal @ other.direction == 0:
         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:

返回: Plane3: 平面

源碼於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

説明: 判断两个平面是否平行。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源碼於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

説明: 平面的法向量。

返回: Vector3: 法向量

源碼於GitHub上查看
python
@property
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3

説明: 计算平行于该平面且过指定点的平面。

變數説明:

返回: Plane3: 平面

源碼於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool

説明: 判断两个平面是否平行。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源碼於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3

説明: 平面的法向量。

返回: Vector3: 法向量

源碼於GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

變數説明:

返回: Plane3: 平面

源碼於GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

變數説明:

返回: Plane3: 平面

源碼於GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     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 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源碼於GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3

説明: 工厂函数 由三点构造平面。

變數説明:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源碼於GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     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 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源碼於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3

説明: 工厂函数 由两直线构造平面。

變數説明:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源碼於GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     v1 = l1.direction
     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:

返回: 平面

源碼於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3

説明: 工厂函数 由点和直线构造平面。

變數説明:

返回: 平面

源碼於GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

源碼於GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None

源碼於GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method self & other: Plane3 => Line3 | None

源碼於GitHub上查看
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None

源碼於GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method self & other

説明: 取两平面的交集(人话:交线)

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼於GitHub上查看
python
def __and__(self, other):
+    ...

method self & other

説明: 取两平面的交集(人话:交线)

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼於GitHub上查看
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -102,10 +102,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼於GitHub上查看
python
def __eq__(self, other) -> bool:
-    return self.approx(other)

method self & other: Line3 => Point3

源碼於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼於GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.approx(other)

method self & other: Line3 => Point3

源碼於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html index 535ee6d..5db69e6 100644 --- a/zht/api/mp_math/point.html +++ b/zht/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

變數説明:

返回: Vector3: 新的向量

源碼於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/segment.html b/zht/api/mp_math/segment.html index 35be59a..a73a8d5 100644 --- a/zht/api/mp_math/segment.html +++ b/zht/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html index b249d88..8b9d21e 100644 --- a/zht/api/mp_math/utils.html +++ b/zht/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

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- + \ No newline at end of file diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html index 3c04eb8..801dfa1 100644 --- a/zht/api/mp_math/vector.html +++ b/zht/api/mp_math/vector.html @@ -8,8 +8,8 @@ - - + + @@ -79,7 +79,7 @@ return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3

源碼於GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3

説明: 取负。

返回: Vector3: 负向量

源碼於GitHub上查看
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3

  • 説明: 零向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 0)

var x_axis

  • 説明: x轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(1, 0, 0)

var y_axis

  • 説明: y轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 1, 0)

var z_axis

  • 説明: z轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 1)

文檔由 VitePress 構建 | API引用由 litedoc 生成

- + \ No newline at end of file diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html index 5a83f7c..4dfc0e8 100644 --- a/zht/api/particle/index.html +++ b/zht/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/api/presets/index.html b/zht/api/presets/index.html index 2865007..b765cbf 100644 --- a/zht/api/presets/index.html +++ b/zht/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html index 2a7a74c..f3389cd 100644 --- a/zht/api/presets/model/index.html +++ b/zht/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -28,7 +28,7 @@ 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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- + \ No newline at end of file diff --git a/zht/demo/best-practice.html b/zht/demo/best-practice.html index 943b8a2..92abb5f 100644 --- a/zht/demo/best-practice.html +++ b/zht/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/guide/index.html b/zht/guide/index.html index c61f0d9..a6f833a 100644 --- a/zht/guide/index.html +++ b/zht/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
Skip to content

开始不了一点

12x111

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- + \ No newline at end of file diff --git a/zht/index.html b/zht/index.html index 538ebe3..ddffd33 100644 --- a/zht/index.html +++ b/zht/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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MBCP

更多基礎變化粒子

用於幾何運算和 當個創世神 粒子製作的軟體庫

MBCP logo

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- + \ No newline at end of file diff --git a/zht/refer/index.html b/zht/refer/index.html index 90ab2bb..7aea1b7 100644 --- a/zht/refer/index.html +++ b/zht/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@
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Reference

Help us to improve the documentation

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