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✨ 支持Liteyuki Docstring
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@ -1,5 +1,5 @@
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# -*- coding: utf-8 -*-
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"""
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本模块塞了一些预设的粒子生成器
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本模块是主模块,用于导入所有模块
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"""
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from .mp_math import *
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@ -2,13 +2,13 @@
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"""
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本包定义了一些常用的导入,可直接从`mbcp.mp_math`导入使用
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导入的类有:
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- `AnyAngle`:任意角
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- `CurveEquation`:曲线方程
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- `Line3`:三维直线
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- `Plane3`:三维平面
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- `Point3`:三维点
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- `Segment3`:三维线段
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- `Vector3`:三维向量
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- [`AnyAngle`](./angle#class-anyangle):任意角度
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- [`CurveEquation`](./equation#class-curveequation):曲线方程
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- [`Line3`](./line#class-line3):三维直线
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- [`Plane3`](./plane#class-plane3):三维平面
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- [`Point3`](./point#class-point3):三维点
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- [`Segment3`](./segment#class-segment3):三维线段
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- [`Vector3`](./vector#class-vector3):三维向量
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"""
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from .angle import AnyAngle
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from .const import *
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@ -13,9 +13,9 @@ class CurveEquation:
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"""
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曲线方程。
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Args:
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x_func: x函数
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y_func: y函数
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z_func: z函数
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x_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): x函数
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y_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): y函数
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z_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): z函数
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"""
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self.x_func = x_func
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self.y_func = y_func
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@ -46,7 +46,7 @@ def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...],
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> 目前数学界对于一个函数的导函数并没有通解的说法,因此该函数的稳定性有待提升
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Args:
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func: 函数
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func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): N元函数
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var: 变量位置,可为整数(一阶偏导)或整数元组(高阶偏导)
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epsilon: 偏移量
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Returns:
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@ -15,8 +15,8 @@ def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSI
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> 已知一个函数$f(x, y, z)$,则其在点$(x_0, y_0, z_0)$处的梯度向量为:
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$\nabla f(x_0, y_0, z_0) = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)$
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Args:
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func: 三元函数
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p: 点
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func ([`ThreeSingleVarsFunc`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
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p ([`Point3`](./point#class-point3)): 点
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epsilon: 偏移量
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Returns:
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梯度
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@ -33,8 +33,8 @@ def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
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> [!tip]
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> 有关函数柯里化,可参考[函数式编程--柯理化(Currying)](https://zhuanlan.zhihu.com/p/355859667)
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Args:
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func: 函数
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*args: 参数
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func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数
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*args ([`Var`](./mp_math_typing#var-var)): 参数
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Returns:
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柯里化后的函数
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Examples:
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@ -20,8 +20,8 @@ class Line3:
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"""
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三维空间中的直线。由一个点和一个方向向量确定。
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Args:
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point: 直线上的一点
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direction: 直线的方向向量
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point ([`Point3`](./point#class-point3)): 直线上的一点
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direction ([`Vector3`](./vector#class-vector3)): 方向向量
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"""
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self.point = point
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self.direction = direction
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@ -30,10 +30,10 @@ class Line3:
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"""
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判断两条直线是否近似相等。
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Args:
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other: 另一条直线
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epsilon: 误差
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other ([`Line3`](./line#class-line3)): 另一条直线
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epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
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Returns:
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是否近似相等
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[`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
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"""
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return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
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@ -41,11 +41,9 @@ class Line3:
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"""
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计算直线和直线之间的夹角。
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Args:
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other: 另一条直线
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other ([`Line3`](./line#class-line3)): 另一条直线
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Returns:
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夹角弧度
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Raises:
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TypeError: 不支持的类型
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[`AnyAngle`](./angle#class-anyangle): 夹角
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"""
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return self.direction.cal_angle(other.direction)
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@ -53,12 +51,11 @@ class Line3:
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"""
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计算直线和直线或点之间的距离。
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Args:
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other: 平行直线或点
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other ([`Line3`](./line#class-line3) | [`Point3`](./point#class-point3)): 另一条直线或点
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Returns:
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距离
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[`float`](https%3A//docs.python.org/3/library/functions.html#float): 距离
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Raises:
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TypeError: 不支持的类型
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[`TypeError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
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"""
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if isinstance(other, Line3):
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# 相交/重合 = 0;平行和异面需要计算距离
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@ -84,12 +81,12 @@ class Line3:
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"""
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计算两条直线的交点。
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Args:
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other: 另一条直线
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other ([`Line3`](./line#class-line3)): 另一条直线
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Returns:
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交点
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[`Point3`](./point#class-point3): 交点
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Raises:
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ValueError: 直线平行
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ValueError: 直线不共面
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[`ValueError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
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`ValueError`: 直线不共面
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"""
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if self.is_parallel(other):
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raise ValueError("Lines are parallel and do not intersect.")
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@ -102,9 +99,9 @@ class Line3:
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"""
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计算直线经过指定点p的垂线。
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Args:
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point: 指定点
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point ([`Point3`](./point#class-point3)): 指定点
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Returns:
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垂线
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[`Line3`](./line#class-line3): 垂线
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"""
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return Line3(point, self.direction.cross(point - self.point))
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@ -112,9 +109,9 @@ class Line3:
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"""
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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。
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Args:
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t: 参数t
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t ([`RealNumber`](./mp_math_typing#var-realnumber)): 参数t
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Returns:
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点
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[`Point3`](./point#class-point3): 点
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"""
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return self.point + t * self.direction
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@ -122,7 +119,7 @@ class Line3:
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"""
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获取直线的参数方程。
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Returns:
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x(t), y(t), z(t)
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[`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
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"""
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return (lambda t: self.point.x + self.direction.x * t,
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lambda t: self.point.y + self.direction.y * t,
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@ -132,10 +129,10 @@ class Line3:
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"""
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判断两条直线是否近似平行。
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Args:
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other: 另一条直线
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epsilon: 误差
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other ([`Line3`](./line#class-line3)): 另一条直线
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epsilon ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
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Returns:
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是否近似平行
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[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
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"""
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return self.direction.is_approx_parallel(other.direction, epsilon)
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@ -143,9 +140,9 @@ class Line3:
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"""
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判断两条直线是否平行。
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Args:
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other: 另一条直线
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other ([`Line3`](./line#class-line3)): 另一
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Returns:
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是否平行
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[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
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"""
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return self.direction.is_parallel(other.direction)
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@ -153,9 +150,9 @@ class Line3:
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"""
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判断两条直线是否共线。
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Args:
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other: 另一条直线
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other ([`Line3`](./line#class-line3)): 另一
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Returns:
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是否共线
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[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
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"""
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return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
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@ -163,9 +160,9 @@ class Line3:
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"""
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判断点是否在直线上。
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Args:
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point: 点
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point ([`Point3`](./point#class-point3)): 点
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Returns:
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是否在直线上
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[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
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"""
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return (point - self.point).is_parallel(self.direction)
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@ -174,9 +171,9 @@ class Line3:
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判断两条直线是否共面。
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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。
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Args:
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other: 另一条直线
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other ([`Line3`](./line#class-line3)): 另一
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Returns:
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是否共面
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[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
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"""
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return self.direction.cross(other.direction) @ (self.point - other.point) == 0
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@ -203,10 +200,10 @@ class Line3:
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"""
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工厂函数 由两点构造直线。
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Args:
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p1: 点1
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p2: 点2
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p1 ([`Point3`](./point#class-point3)): 点1
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p2 ([`Point3`](./point#class-point3)): 点2
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Returns:
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直线
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[`Line3`](./line#class-line3): 直线
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"""
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direction = p2 - p1
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return cls(p1, direction)
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@ -215,9 +212,9 @@ class Line3:
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"""
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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。
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Args:
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other: 另一条直线
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other ([`Line3`](./line#class-line3)): 另一条直线
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Returns:
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交点
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[`Line3`](./line#class-line3) | [`Point3`](./point#class-point3) | [`None`](https://docs.python.org/3/library/constants.html#None): 交集
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"""
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if self.is_collinear(other):
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return self
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@ -232,10 +229,9 @@ class Line3:
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v1 // v2 ∧ (p1 - p2) // v1
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Args:
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other:
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other ([`Line3`](./line#class-line3)): 另一条直线
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Returns:
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[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
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"""
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return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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@ -243,7 +239,7 @@ class Line3:
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"""
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返回点向式(x-x0)
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Returns:
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[`str`](https%3A//docs.python.org/3/library/functions.html#str): 点向式
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"""
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s = "Line3: "
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if self.direction.x != 0:
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@ -255,4 +251,9 @@ class Line3:
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return s
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def __repr__(self):
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"""
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返回直线的字符串表示。
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Returns:
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[`str`](https%3A//docs.python.org/3/library/functions.html#str) 字符串表示
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"""
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return f"Line3({self.point}, {self.direction})"
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@ -21,10 +21,10 @@ class Plane3:
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"""
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平面方程:ax + by + cz + d = 0
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Args:
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a: x系数
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b: y系数
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c: z系数
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d: 常数项
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a ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
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b (`float`): y系数
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c (`float`): z系数
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d (`float`): 常数项
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"""
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self.a = a
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self.b = b
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@ -35,9 +35,9 @@ class Plane3:
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"""
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判断两个平面是否近似相等。
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Args:
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other: 另一个平面
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other ([`Plane3`](./plane#class-plane3)): 另一个平面
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Returns:
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是否近似相等
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[`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
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"""
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if self.a != 0:
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k = other.a / self.a
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@ -55,11 +55,11 @@ class Plane3:
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"""
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计算平面与平面之间的夹角。
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Args:
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other: 另一个平面
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other ([`Line3`](./line#class-line3) | [`Plane3`](./plane#class-plane3)): 另一个平面或直线
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Returns:
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夹角弧度
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[`AnyAngle`](./angle#class-anyangle): 夹角
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Raises:
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TypeError: 不支持的类型
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[`TypeError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
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"""
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if isinstance(other, Line3):
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return self.normal.cal_angle(other.direction).complementary
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@ -72,11 +72,11 @@ class Plane3:
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"""
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计算平面与平面或点之间的距离。
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Args:
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other: 另一个平面或点
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other ([`Plane3`](./plane#class-plane3) | [`Point3`](./point#class-point3)): 另一个平面或点
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Returns:
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距离
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[`float`](https%3A//docs.python.org/3/library/functions.html#float): 距离
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Raises:
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TypeError: 不支持的类型
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[`TypeError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
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"""
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if isinstance(other, Plane3):
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return 0
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@ -89,10 +89,11 @@ class Plane3:
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"""
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计算两平面的交线。
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Args:
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other: 另一个平面
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other ([`Plane3`](./plane#class-plane3)): 另一个平面
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Returns:
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两平面的交线
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[`Line3`](./line#class-line3): 交线
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Raises:
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[`ValueError`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
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"""
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if self.normal.is_parallel(other.normal):
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raise ValueError("Planes are parallel and have no intersection.")
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@ -121,11 +122,11 @@ class Plane3:
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"""
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计算平面与直线的交点。
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Args:
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other: 不与平面平行或在平面上的直线
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other ([`Line3`](./line#class-line3)): 直线
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Returns:
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交点
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[`Point3`](./point#class-point3): 交点
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Raises:
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ValueError: 平面与直线平行或重合
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[`ValueError`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
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"""
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# 若平面的法向量与直线方向向量垂直,则直线与平面平行或重合
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if self.normal @ other.direction == 0:
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@ -141,9 +142,9 @@ class Plane3:
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"""
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计算平行于该平面且过指定点的平面。
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Args:
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point: 指定点
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point ([`Point3`](./point#class-point3)): 指定点
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Returns:
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所求平面
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[`Plane3`](./plane#class-plane3): 平面
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"""
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return Plane3.from_point_and_normal(point, self.normal)
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|
||||
@ -151,9 +152,9 @@ class Plane3:
|
||||
"""
|
||||
判断两个平面是否平行。
|
||||
Args:
|
||||
other: 另一个平面
|
||||
other ([`Plane3`](./plane#class-plane3)): 另一个平面
|
||||
Returns:
|
||||
是否平行
|
||||
[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
|
||||
"""
|
||||
return self.normal.is_parallel(other.normal)
|
||||
|
||||
@ -162,7 +163,7 @@ class Plane3:
|
||||
"""
|
||||
平面的法向量。
|
||||
Returns:
|
||||
法向量
|
||||
[`Vector3`](./vector#class-vector3): 法向量
|
||||
"""
|
||||
return Vector3(self.a, self.b, self.c)
|
||||
|
||||
@ -171,10 +172,10 @@ class Plane3:
|
||||
"""
|
||||
工厂函数 由点和法向量构造平面(点法式构造)。
|
||||
Args:
|
||||
point: 平面上的一点
|
||||
normal: 法向量
|
||||
point ([`Point3`](./point#class-point3)): 平面上一点
|
||||
normal ([`Vector3`](./vector#class-vector3)): 法向量
|
||||
Returns:
|
||||
平面
|
||||
[`Plane3`](./plane#class-plane3): 平面
|
||||
"""
|
||||
a, b, c = normal.x, normal.y, normal.z
|
||||
d = -a * point.x - b * point.y - c * point.z # d = -ax - by - cz
|
||||
@ -185,9 +186,9 @@ class Plane3:
|
||||
"""
|
||||
工厂函数 由三点构造平面。
|
||||
Args:
|
||||
p1: 点1
|
||||
p2: 点2
|
||||
p3: 点3
|
||||
p1 ([`Point3`](./point#class-point3)): 点1
|
||||
p2 (`Point3`): 点2
|
||||
p3 (`Point3`): 点3
|
||||
Returns:
|
||||
平面
|
||||
"""
|
||||
@ -203,8 +204,8 @@ class Plane3:
|
||||
"""
|
||||
工厂函数 由两直线构造平面。
|
||||
Args:
|
||||
l1: 直线1
|
||||
l2: 直线2
|
||||
l1 ([`Line3`](./line#class-line3)): 直线
|
||||
l2 (`Line3`): 直线
|
||||
Returns:
|
||||
平面
|
||||
"""
|
||||
@ -219,17 +220,27 @@ class Plane3:
|
||||
"""
|
||||
工厂函数 由点和直线构造平面。
|
||||
Args:
|
||||
point: 面上一点
|
||||
line: 面上直线,不包含点
|
||||
point ([`Point3`](./point#class-point3)): 平面上一点
|
||||
line ([`Line3`](./line#class-line3)): 直线
|
||||
Returns:
|
||||
平面
|
||||
"""
|
||||
return cls.from_point_and_normal(point, line.direction)
|
||||
|
||||
def __repr__(self):
|
||||
"""
|
||||
返回平面的字符串表示。
|
||||
Returns:
|
||||
[`str`](https%3A//docs.python.org/3/library/functions.html#str): 字符串表示
|
||||
"""
|
||||
return f"Plane3({self.a}, {self.b}, {self.c}, {self.d})"
|
||||
|
||||
def __str__(self):
|
||||
"""
|
||||
返回平面的字符串表示。
|
||||
Returns:
|
||||
[`str`](https%3A//docs.python.org/3/library/functions.html#str): 字符串表示
|
||||
"""
|
||||
s = "Plane3: "
|
||||
if self.a != 0:
|
||||
s += f"{sign(self.a, only_neg=True)}{abs(self.a)}x"
|
||||
@ -253,9 +264,11 @@ class Plane3:
|
||||
"""
|
||||
取两平面的交集(人话:交线)
|
||||
Args:
|
||||
other:
|
||||
other ([`Line3`](./line#class-line3) | [`Plane3`](./plane#class-plane3)): 另一个平面或直线
|
||||
Returns:
|
||||
不平行平面的交线,平面平行返回None
|
||||
[`Line3`](./line#class-line3) | [`Point3`](./point#class-point3) | [`None`](https%3A//docs.python.org/3/library/constants.html#None): 交集
|
||||
Raises:
|
||||
[`TypeError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
|
||||
"""
|
||||
if isinstance(other, Plane3):
|
||||
if self.normal.is_parallel(other.normal):
|
||||
@ -269,6 +282,13 @@ class Plane3:
|
||||
raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
|
||||
|
||||
def __eq__(self, other) -> bool:
|
||||
"""
|
||||
判断两个平面是否等价。
|
||||
Args:
|
||||
other ([`Plane3`](./plane#class-plane3)): 另一个平面
|
||||
Returns:
|
||||
[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
|
||||
"""
|
||||
return self.approx(other)
|
||||
|
||||
def __rand__(self, other: 'Line3') -> 'Point3':
|
||||
|
@ -16,9 +16,9 @@ class Point3:
|
||||
"""
|
||||
笛卡尔坐标系中的点。
|
||||
Args:
|
||||
x: x 坐标
|
||||
y: y 坐标
|
||||
z: z 坐标
|
||||
x ([`float`](https://docs.python.org/3/library/functions.html#float)): x 坐标
|
||||
y (`float`): y 坐标
|
||||
z (`float`): z 坐标
|
||||
"""
|
||||
self.x = x
|
||||
self.y = y
|
||||
@ -28,15 +28,19 @@ class Point3:
|
||||
"""
|
||||
判断两个点是否近似相等。
|
||||
Args:
|
||||
other:
|
||||
epsilon:
|
||||
|
||||
other ([`Point3`](./point#class-point3)): 另一个点
|
||||
epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
|
||||
Returns:
|
||||
是否近似相等
|
||||
[`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
|
||||
"""
|
||||
return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
|
||||
|
||||
def __str__(self):
|
||||
"""
|
||||
点的字符串表示。
|
||||
Returns:
|
||||
[`str`](https://docs.python.org/3/library/functions.html#str): 字符串
|
||||
"""
|
||||
return f"Point3({self.x}, {self.y}, {self.z})"
|
||||
|
||||
@overload
|
||||
@ -52,8 +56,9 @@ class Point3:
|
||||
P + V -> P
|
||||
P + P -> P
|
||||
Args:
|
||||
other:
|
||||
other ([`Vector3`](./vector#class-vector3) | [`Point3`](./point#class-point3)): 另一个点或向量
|
||||
Returns:
|
||||
[`Point3`](./point#class-point3): 新的点
|
||||
"""
|
||||
return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
|
||||
|
||||
@ -61,8 +66,9 @@ class Point3:
|
||||
"""
|
||||
判断两个点是否相等。
|
||||
Args:
|
||||
other:
|
||||
other ([`Point3`](./point#class-point3)): 另一个点
|
||||
Returns:
|
||||
[`bool`](https://docs.python.org/3/library/functions.html#bool): 是否相等
|
||||
"""
|
||||
return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
|
||||
|
||||
@ -70,11 +76,11 @@ class Point3:
|
||||
"""
|
||||
P - P -> V
|
||||
|
||||
P - V -> P 已在 :class:`Vector3` 中实现
|
||||
P - V -> P 已在 [`Vector3`](./vector#class-vector3) 中实现
|
||||
Args:
|
||||
other:
|
||||
other ([`Point3`](./point#class-point3)): 另一个点
|
||||
Returns:
|
||||
|
||||
[`Vector3`](./vector#class-vector3): 新的向量
|
||||
"""
|
||||
from .vector import Vector3
|
||||
return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
|
||||
|
@ -14,8 +14,9 @@ class Segment3:
|
||||
def __init__(self, p1: "Point3", p2: "Point3"):
|
||||
"""
|
||||
三维空间中的线段。
|
||||
:param p1:
|
||||
:param p2:
|
||||
Args:
|
||||
p1 ([`Point3`](./point#class-point3)): 线段的一个端点
|
||||
p2 ([`Point3`](./point#class-point3)): 线段的另一个端点
|
||||
"""
|
||||
self.p1 = p1
|
||||
self.p2 = p2
|
||||
@ -28,7 +29,17 @@ class Segment3:
|
||||
self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
|
||||
|
||||
def __repr__(self):
|
||||
"""
|
||||
线段的字符串表示(可执行)。
|
||||
Returns:
|
||||
[`str`](https://docs.python.org/3/library/functions.html#str): 字符串
|
||||
"""
|
||||
return f"Segment3({self.p1}, {self.p2})"
|
||||
|
||||
def __str__(self):
|
||||
"""
|
||||
线段的字符串表示。
|
||||
Returns:
|
||||
[`str`](https://docs.python.org/3/library/functions.html#str): 字符串
|
||||
"""
|
||||
return f"Segment3({self.p1} -> {self.p2})"
|
||||
|
@ -18,12 +18,12 @@ def clamp(x: float, min_: float, max_: float) -> float:
|
||||
"""
|
||||
区间限定函数
|
||||
Args:
|
||||
x: 待限定的值
|
||||
min_: 最小值
|
||||
max_: 最大值
|
||||
x ([`float`](https://docs.python.org/3/library/functions.html#float)): 值
|
||||
min_ (`float`): 最小值
|
||||
max_ (`float`): 最大值
|
||||
|
||||
Returns:
|
||||
限制后的值
|
||||
`float`: 限定在区间内的值
|
||||
"""
|
||||
return max(min(x, max_), min_)
|
||||
|
||||
@ -31,10 +31,14 @@ def clamp(x: float, min_: float, max_: float) -> float:
|
||||
class Approx:
|
||||
"""
|
||||
用于近似比较对象
|
||||
|
||||
已实现对象 实数 Vector3 Point3 Plane3 Line3
|
||||
"""
|
||||
def __init__(self, value: RealNumber):
|
||||
"""
|
||||
用于近似比较对象
|
||||
Args:
|
||||
value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
|
||||
"""
|
||||
self.value = value
|
||||
|
||||
def __eq__(self, other):
|
||||
@ -60,11 +64,11 @@ def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool:
|
||||
"""
|
||||
判断两个数是否近似相等。或包装一个实数,用于判断是否近似于0。
|
||||
Args:
|
||||
x: 数1
|
||||
y: 数2
|
||||
epsilon: 误差
|
||||
x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数1
|
||||
y (`float`): 数2
|
||||
epsilon (`float`): 误差
|
||||
Returns:
|
||||
是否近似相等
|
||||
[`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
|
||||
"""
|
||||
return abs(x - y) < epsilon
|
||||
|
||||
@ -72,10 +76,10 @@ def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool:
|
||||
def sign(x: float, only_neg: bool = False) -> str:
|
||||
"""获取数的符号。
|
||||
Args:
|
||||
x: 数
|
||||
only_neg: 是否只返回负数的符号
|
||||
x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
|
||||
only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
|
||||
Returns:
|
||||
符号 + - ""
|
||||
[`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
|
||||
"""
|
||||
if x > 0:
|
||||
return "+" if not only_neg else ""
|
||||
@ -91,10 +95,10 @@ def sign_format(x: float, only_neg: bool = False) -> str:
|
||||
1 -> +1
|
||||
0 -> ""
|
||||
Args:
|
||||
x: 数
|
||||
only_neg: 是否只返回负数的符号
|
||||
x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
|
||||
only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
|
||||
Returns:
|
||||
符号 + - ""
|
||||
[`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
|
||||
"""
|
||||
if x > 0:
|
||||
return f"+{x}" if not only_neg else f"{x}"
|
||||
|
@ -43,9 +43,9 @@ class Vector3:
|
||||
"""
|
||||
计算两个向量之间的夹角。
|
||||
Args:
|
||||
other: 另一个向量
|
||||
other ([`Vector3`](#class-vector3)): 另一个向量
|
||||
Returns:
|
||||
夹角
|
||||
[`AnyAngle`](./angle#class-anyangle): 夹角
|
||||
"""
|
||||
return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
|
||||
|
||||
@ -65,9 +65,9 @@ class Vector3:
|
||||
``x2 y2 z2``
|
||||
|
||||
Args:
|
||||
other:
|
||||
other ([`Vector3`](#class-vector3)): 另一个向量
|
||||
Returns:
|
||||
行列式的结果
|
||||
[`Vector3`](#class-vector3): 叉乘结果
|
||||
"""
|
||||
return Vector3(self.y * other.z - self.z * other.y,
|
||||
self.z * other.x - self.x * other.z,
|
||||
@ -77,10 +77,10 @@ class Vector3:
|
||||
"""
|
||||
判断两个向量是否近似平行。
|
||||
Args:
|
||||
other: 另一个向量
|
||||
epsilon: 允许的误差
|
||||
other ([`Vector3`](#class-vector3)): 另一个向量
|
||||
epsilon ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
|
||||
Returns:
|
||||
是否近似平行
|
||||
[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
|
||||
"""
|
||||
return self.cross(other).length < epsilon
|
||||
|
||||
@ -88,9 +88,9 @@ class Vector3:
|
||||
"""
|
||||
判断两个向量是否平行。
|
||||
Args:
|
||||
other: 另一个向量
|
||||
other ([`Vector3`](#class-vector3)): 另一个向量
|
||||
Returns:
|
||||
是否平行
|
||||
[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
|
||||
"""
|
||||
return self.cross(other).approx(zero_vector3)
|
||||
|
||||
@ -110,6 +110,7 @@ class Vector3:
|
||||
"""
|
||||
返回numpy数组
|
||||
Returns:
|
||||
[`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
|
||||
"""
|
||||
|
||||
return np.array([self.x, self.y, self.z])
|
||||
@ -119,7 +120,7 @@ class Vector3:
|
||||
"""
|
||||
向量的模。
|
||||
Returns:
|
||||
模
|
||||
[`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
|
||||
"""
|
||||
return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
|
||||
|
||||
@ -128,7 +129,7 @@ class Vector3:
|
||||
"""
|
||||
获取该向量的单位向量。
|
||||
Returns:
|
||||
单位向量
|
||||
[`Vector3`](#class-vector3): 单位向量
|
||||
"""
|
||||
return self / self.length
|
||||
|
||||
@ -148,9 +149,9 @@ class Vector3:
|
||||
V + P -> P\n
|
||||
V + V -> V
|
||||
Args:
|
||||
other:
|
||||
other ([`Vector3`](#class-vector3) | [`Point3`](./point#class-point3)): 另一个向量或点
|
||||
Returns:
|
||||
|
||||
[`Vector3`](#class-vector3) | [`Point3`](./point#class-point3): 新的向量或点
|
||||
"""
|
||||
if isinstance(other, Vector3):
|
||||
return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
|
||||
@ -163,9 +164,9 @@ class Vector3:
|
||||
"""
|
||||
判断两个向量是否相等。
|
||||
Args:
|
||||
other:
|
||||
other ([`Vector3`](#class-vector3)): 另一个向量
|
||||
Returns:
|
||||
是否相等
|
||||
[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
|
||||
"""
|
||||
return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
|
||||
|
||||
@ -173,8 +174,10 @@ class Vector3:
|
||||
"""
|
||||
P + V -> P\n
|
||||
别去点那边实现了。
|
||||
:param other:
|
||||
:return:
|
||||
Args:
|
||||
other ([`Point3`](./point#class-point3)): 另一个点
|
||||
Returns:
|
||||
[`Point3`](./point#class-point3): 新的点
|
||||
"""
|
||||
return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
|
||||
|
||||
@ -191,8 +194,9 @@ class Vector3:
|
||||
V - P -> P\n
|
||||
V - V -> V
|
||||
Args:
|
||||
other:
|
||||
other ([`Vector3`](#class-vector3) | [`Point3`](./point#class-point3)): 另一个向量或点
|
||||
Returns:
|
||||
[`Vector3`](#class-vector3) | [`Point3`](./point#class-point3): 新的向量
|
||||
"""
|
||||
if isinstance(other, Vector3):
|
||||
return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
|
||||
@ -205,9 +209,9 @@ class Vector3:
|
||||
"""
|
||||
P - V -> P
|
||||
Args:
|
||||
other:
|
||||
other ([`Point3`](./point#class-point3)): 另一个点
|
||||
Returns:
|
||||
|
||||
[`Point3`](./point#class-point3): 新的点
|
||||
"""
|
||||
|
||||
if isinstance(other, Point3):
|
||||
@ -227,9 +231,9 @@ class Vector3:
|
||||
"""
|
||||
数组运算 非点乘。点乘使用@,叉乘使用cross。
|
||||
Args:
|
||||
other:
|
||||
|
||||
other ([`Vector3`](#class-vector3) | [`float`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
|
||||
Returns:
|
||||
[`Vector3`](#class-vector): 数组运算结果
|
||||
"""
|
||||
|
||||
if isinstance(other, Vector3):
|
||||
@ -246,21 +250,37 @@ class Vector3:
|
||||
"""
|
||||
点乘。
|
||||
Args:
|
||||
other:
|
||||
other ([`Vector3`](#class-vector3)): 另一个向量
|
||||
Returns:
|
||||
[`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
|
||||
"""
|
||||
return self.x * other.x + self.y * other.y + self.z * other.z
|
||||
|
||||
def __truediv__(self, other: RealNumber) -> 'Vector3':
|
||||
return Vector3(self.x / other, self.y / other, self.z / other)
|
||||
|
||||
def __neg__(self):
|
||||
def __neg__(self) -> 'Vector3':
|
||||
"""
|
||||
取负。
|
||||
Returns:
|
||||
[`Vector3`](#class-vector3): 负向量
|
||||
"""
|
||||
return Vector3(-self.x, -self.y, -self.z)
|
||||
|
||||
def __repr__(self):
|
||||
def __repr__(self) -> str:
|
||||
"""
|
||||
向量的字符串表示(可执行)。
|
||||
Returns:
|
||||
[`str`](https%3A//docs.python.org/3/library/functions.html#str): 字符串
|
||||
"""
|
||||
return f"Vector3({self.x}, {self.y}, {self.z})"
|
||||
|
||||
def __str__(self):
|
||||
def __str__(self) -> str:
|
||||
"""
|
||||
向量的字符串表示。
|
||||
Returns:
|
||||
[`str`](https%3A//docs.python.org/3/library/functions.html#str): 字符串
|
||||
"""
|
||||
return f"Vector3({self.x}, {self.y}, {self.z})"
|
||||
|
||||
|
||||
|
@ -1,10 +1,4 @@
|
||||
# -*- coding: utf-8 -*-
|
||||
"""
|
||||
Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
|
||||
|
||||
@Time : 2024/8/12 下午9:12
|
||||
@Author : snowykami
|
||||
@Email : snowykami@outlook.com
|
||||
@File : __init__.py
|
||||
@Software: PyCharm
|
||||
本模块塞了一些预设
|
||||
"""
|
Loading…
Reference in New Issue
Block a user