```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 ``` ```#!/usr/bin/python3 from numbers import Number from math import acos __all__ = ['Vector3D', 'iVector', 'jVector', 'kVector'] class Vector3D: def __init__(self, i=0, j=0, k=0): self._i = i self._j = j self._k = k @classmethod def CrossProduct(cls, uVector, vVector): # print(uVector, vVector) i = uVector._j * vVector._k - uVector._k * vVector._j # print(uVector._j * vVector._k, uVector._k * vVector._j, i) j = uVector._k * vVector._i - uVector._i * vVector._k # print(uVector._k * vVector._i, uVector._i * vVector._k, j) k = uVector._i * vVector._j - uVector._j * vVector._i # print(uVector._i * vVector._j, uVector._j * vVector._i, k) return cls(i, j, k) def LeftCross(self, vVector): return self.CrossProduct(self, vVector) def RightCross(self, uVector): return self.CrossProduct(uVector, self) @classmethod def DotProduct(cls, uVector, vVector): return uVector._i * vVector._i + uVector._j * vVector._j + uVector._k * vVector._k def Dot(self, vVector): return self.DotProduct(self, vVector) def ScalarMultiply(self, Scalar): return Vector3D(self._i * Scalar, self._j * Scalar, self._k * Scalar) def DivideByScalar(self, Scalar): return self.ScalarMultiply(1. / Scalar) def Magnitude(self): return (self._i ** 2. + self._j ** 2. + self._k ** 2.) ** .5 def UnitVector(self): return self / self.Magnitude() def AngleTo(self, vVector): Theta = acos(self.Dot(vVector) / (self.Magnitude() * vVector.Magnitude())) return Theta def AddVector(self, vVector): return Vector3D(self._i + vVector._i, self._j + vVector._j, self._k + vVector._k) def SubtractVector(self, vVector): return self.AddVector(-vVector) def Negate(self): return Vector3D(-self._i, -self._j, -self._k) def ConvertToFrame(self, iVector1, jVector1, kVector1): if abs(iVector1.Magnitude() - 1.) > .0001: iVector1 = iVector1.UnitVector() if abs(jVector1.Magnitude() - 1.) > .0001: jVector1 = jVector1.UnitVector() if abs(kVector1.Magnitude() - 1.) > .0001: kVector1 = kVector1.UnitVector() iPart = self.Dot(iVector1) jPart = self.Dot(jVector1) kPart = self.Dot(kVector1) return Vector3D(iPart, jPart, kPart) def GetTuple(self): return (self._i, self._j, self._k) def __neg__(self): return self.Negate() def __mul__(self, vVector): if isinstance(vVector, Vector3D): return self.LeftCross(vVector) if isinstance(vVector, Number): return self.ScalarMultiply(vVector) return NotImplemented def __rmul__(self, uVector): if isinstance(uVector, Vector3D): return self.RightCross(uVector) if isinstance(uVector, Number): return self.ScalarMultiply(uVector) return NotImplemented def __add__(self, vVector): if isinstance(vVector, Vector3D): return self.AddVector(vVector) return NotImplemented def __sub__(self, vVector): if isinstance(vVector, Vector3D): return self.SubtractVector(vVector) return NotImplemented def __truediv__(self, Scalar): if isinstance(Scalar, Number): return self.DivideByScalar(Scalar) return NotImplemented def __eq__(self, vVector): if isinstance(vVector, Vector3D): return (self._i == vVector._i) and (self._j == vVector._j) and (self._k == vVector._k) return NotImplemented def __neq__(self, vVector): return not self.__eq__(vVector) def __round__(self, ndigits): return Vector3D(round(self._i, ndigits), round(self._j, ndigits), round(self._j, ndigits)) def __format__(self, FormatSpec): return("[{0}i, {1}j, {2}k]".format(self._i.__format__(FormatSpec), self._j.__format__(FormatSpec), self._k.__format__(FormatSpec))) def __str__(self): return self.__format__("") def __repr__(self): return("Vector3D({0}, {1}, {2})".format(self._i, self._j, self._k)) iVector = Vector3D(1, 0, 0) jVector = Vector3D(0, 1, 0) kVector = Vector3D(0, 0, 1) if __name__ == "__main__": from random import random uVector = Vector3D(random() * 10. - 5., random() * 10. - 5., random() * 10. - 5.) print("u: {0}".format(uVector)) vVector = Vector3D(random() * 10. - 5., random() * 10. - 5., random() * 10. - 5.) print("v: {0}".format(vVector)) print("u = repr(u) = {0}".format(repr(uVector))) print("u × v = {0}".format(uVector * vVector)) print("v × u = {0}".format(vVector * uVector)) print("u · v = {0}".format(uVector.Dot(vVector))) print("v · u = {0}".format(vVector.Dot(uVector))) print("|u| = {0}".format(uVector.Magnitude())) print("|v| = {0}".format(vVector.Magnitude())) print("û = {0}".format(uVector.UnitVector())) print("|û| = {0}".format(uVector.UnitVector().Magnitude())) print("Angle between u and v: {0}".format(uVector.AngleTo(vVector))) print("Angle between v and u: {0}".format(vVector.AngleTo(uVector))) print("u + v = {0}".format(uVector + vVector)) print("v + u = {0}".format(vVector + uVector)) print("-u = {0}".format(-uVector)) print("u - v = {0}".format(uVector - vVector)) print("v - u = {0}".format(vVector - uVector)) a = random() * 10. - 5. print("a = {0}".format(a)) print("u / a = {0}".format(uVector / a)) ```