mirror of
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295 lines
9.0 KiB
Python
295 lines
9.0 KiB
Python
"""
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本模块定义了3维向量的类Vector3，以及一些常用的向量。
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"""
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import math
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from typing import overload
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import numpy as np
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from .angle import AnyAngle
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from .const import APPROX
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from .mp_math_typing import RealNumber
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from .point import Point3
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from .utils import approx
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class Vector3:
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def __init__(self, x: float, y: float, z: float):
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"""
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3维向量
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Args:
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x: x轴分量
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y: y轴分量
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z: z轴分量
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"""
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self.x = x
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self.y = y
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self.z = z
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def approx(self, other: 'Vector3', epsilon: float = APPROX) -> bool:
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"""
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判断两个向量是否近似相等。
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Args:
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other:
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epsilon:
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Returns:
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是否近似相等
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"""
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return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
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def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
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"""
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计算两个向量之间的夹角。
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Args:
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other ([`Vector3`](#class-vector3)): 另一个向量
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Returns:
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[`AnyAngle`](./angle#class-anyangle): 夹角
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"""
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return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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def cross(self, other: 'Vector3') -> 'Vector3':
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"""
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向量积 叉乘：v1 cross v2 -> v3
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叉乘为0，则两向量平行。
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其余结果的模为平行四边形的面积。
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返回如下行列式的结果：
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``i j k``
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``x1 y1 z1``
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``x2 y2 z2``
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Args:
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other ([`Vector3`](#class-vector3)): 另一个向量
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Returns:
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[`Vector3`](#class-vector3): 叉乘结果
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"""
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return Vector3(self.y * other.z - self.z * other.y,
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self.z * other.x - self.x * other.z,
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self.x * other.y - self.y * other.x)
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def is_approx_parallel(self, other: 'Vector3', epsilon: float = APPROX) -> bool:
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"""
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判断两个向量是否近似平行。
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Args:
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other ([`Vector3`](#class-vector3)): 另一个向量
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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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[`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.cross(other).length < epsilon
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def is_parallel(self, other: 'Vector3') -> bool:
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"""
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判断两个向量是否平行。
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Args:
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other ([`Vector3`](#class-vector3)): 另一个向量
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Returns:
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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.cross(other).approx(zero_vector3)
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def normalize(self):
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"""
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将向量归一化。
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自体归一化，不返回值。
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"""
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length = self.length
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self.x /= length
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self.y /= length
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self.z /= length
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@property
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def np_array(self) -> 'np.ndarray':
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"""
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返回numpy数组
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Returns:
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[`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
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"""
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return np.array([self.x, self.y, self.z])
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@property
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def length(self) -> float:
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"""
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向量的模。
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Returns:
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[`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
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"""
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return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
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@property
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def unit(self) -> 'Vector3':
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"""
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获取该向量的单位向量。
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Returns:
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[`Vector3`](#class-vector3): 单位向量
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"""
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return self / self.length
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def __abs__(self):
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return self.length
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@overload
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def __add__(self, other: 'Vector3') -> 'Vector3':
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...
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@overload
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def __add__(self, other: 'Point3') -> 'Point3':
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...
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def __add__(self, other):
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"""
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V + P -> P\n
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V + V -> V
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Args:
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other ([`Vector3`](#class-vector3) | [`Point3`](./point#class-point3)): 另一个向量或点
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Returns:
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[`Vector3`](#class-vector3) | [`Point3`](./point#class-point3): 新的向量或点
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"""
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if isinstance(other, Vector3):
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return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
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elif isinstance(other, Point3):
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return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
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else:
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raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
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def __eq__(self, other):
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"""
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判断两个向量是否相等。
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Args:
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other ([`Vector3`](#class-vector3)): 另一个向量
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Returns:
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[`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
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"""
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return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
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def __radd__(self, other: 'Point3') -> 'Point3':
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"""
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P + V -> P\n
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别去点那边实现了。
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Args:
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other ([`Point3`](./point#class-point3)): 另一个点
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Returns:
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[`Point3`](./point#class-point3): 新的点
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"""
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return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
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@overload
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def __sub__(self, other: 'Vector3') -> 'Vector3':
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...
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@overload
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def __sub__(self, other: 'Point3') -> "Point3":
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...
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def __sub__(self, other):
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"""
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V - P -> P\n
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V - V -> V
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Args:
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other ([`Vector3`](#class-vector3) | [`Point3`](./point#class-point3)): 另一个向量或点
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Returns:
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[`Vector3`](#class-vector3) | [`Point3`](./point#class-point3): 新的向量
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"""
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if isinstance(other, Vector3):
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return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
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elif isinstance(other, Point3):
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return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
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else:
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raise TypeError(f"unsupported operand type(s) for -: \"Vector3\" and \"{type(other)}\"")
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def __rsub__(self, other: 'Point3'):
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"""
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P - V -> P
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Args:
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other ([`Point3`](./point#class-point3)): 另一个点
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Returns:
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[`Point3`](./point#class-point3): 新的点
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"""
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if isinstance(other, Point3):
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return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
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else:
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raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
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@overload
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def __mul__(self, other: 'Vector3') -> 'Vector3':
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...
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@overload
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def __mul__(self, other: RealNumber) -> 'Vector3':
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...
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def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
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"""
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数组运算 非点乘。点乘使用@，叉乘使用cross。
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Args:
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other ([`Vector3`](#class-vector3) | [`float`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
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Returns:
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[`Vector3`](#class-vector): 数组运算结果
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"""
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if isinstance(other, Vector3):
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return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
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elif isinstance(other, (float, int)):
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return Vector3(self.x * other, self.y * other, self.z * other)
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else:
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raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
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def __rmul__(self, other: 'RealNumber') -> 'Vector3':
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return self.__mul__(other)
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def __matmul__(self, other: 'Vector3') -> 'RealNumber':
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"""
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点乘。
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Args:
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other ([`Vector3`](#class-vector3)): 另一个向量
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Returns:
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[`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
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"""
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return self.x * other.x + self.y * other.y + self.z * other.z
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def __truediv__(self, other: RealNumber) -> 'Vector3':
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return Vector3(self.x / other, self.y / other, self.z / other)
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def __neg__(self) -> 'Vector3':
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"""
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取负。
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Returns:
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[`Vector3`](#class-vector3): 负向量
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"""
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return Vector3(-self.x, -self.y, -self.z)
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def __repr__(self) -> str:
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"""
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向量的字符串表示(可执行)。
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Returns:
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[`str`](https%3A//docs.python.org/3/library/functions.html#str): 字符串
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"""
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return f"Vector3({self.x}, {self.y}, {self.z})"
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def __str__(self) -> str:
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"""
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向量的字符串表示。
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Returns:
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[`str`](https%3A//docs.python.org/3/library/functions.html#str): 字符串
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"""
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return f"Vector3({self.x}, {self.y}, {self.z})"
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zero_vector3: Vector3 = Vector3(0, 0, 0)
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"""零向量"""
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x_axis: Vector3 = Vector3(1, 0, 0)
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"""x轴单位向量"""
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y_axis: Vector3 = Vector3(0, 1, 0)
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"""y轴单位向量"""
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z_axis: Vector3 = Vector3(0, 0, 1)
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"""z轴单位向量"""
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