C++实现一个Vector3空间向量类

Vector2,3,4类在DirectX中都有现成的可以调用，不过要实现其中的功能其实也不难，也都是一些简单的数学知识罢了。

本文用C++实现一个简单的Vector3类的功能，暂时有的功能是：

1 + - * /算术运算

2 向量的数量积，又叫：点乘

3 向量的向量积，又叫：叉乘

4 向量单位化（normalization)

 

//Vecotr3.h#pragma onceextern const double uZero;class Vector3{float x, y, z;public:Vector3():x(0), y(0), z(0){}Vector3(float x1, float y1, float z1):x(x1), y(y1), z(z1){}Vector3(const Vector3 &v);~Vector3();void operator=(const Vector3 &v);Vector3 operator+(const Vector3 &v);Vector3 operator-(const Vector3 &v);Vector3 operator/(const Vector3 &v);Vector3 operator*(const Vector3 &v);Vector3 operator+(float f);Vector3 operator-(float f);Vector3 operator/(float f);Vector3 operator*(float f);float dot(const Vector3 &v);float length();void normalize();Vector3 crossProduct(const Vector3 &v);void printVec3();};

//Vector3.cpp#include"Plane.h"#include<iostream>const double uZero = 1e-6;//复制构造函数，必须为常量引用参数，否则编译不通过Vector3::Vector3(const Vector3 &v):x(v.x), y(v.y), z(v.z){}Vector3::~Vector3(){}void Vector3::operator=(const Vector3 &v){x = v.x;y = v.y;z = v.z;}Vector3 Vector3::operator+(const Vector3 &v){return Vector3(x+v.x, y+v.y, z+v.z);}Vector3 Vector3::operator-(const Vector3 &v){return Vector3(x-v.x, y-v.y, z-v.z);}Vector3 Vector3::operator/(const Vector3 &v){if (fabsf(v.x) <= uZero || fabsf(v.y) <= uZero || fabsf(v.z) <= uZero){std::cerr<<"Over flow!\n";return *this;}return Vector3(x/v.x, y/v.y, z/v.z);}Vector3 Vector3::operator*(const Vector3 &v){return Vector3(x*v.x, y*v.y, z*v.z);}Vector3 Vector3::operator+(float f){return Vector3(x+f, y+f, z+f);}Vector3 Vector3::operator-(float f){return Vector3(x-f, y-f, z-f);}Vector3 Vector3::operator/(float f){if (fabsf(f) < uZero){std::cerr<<"Over flow!\n";return *this;}return Vector3(x/f, y/f, z/f);}Vector3 Vector3::operator*(float f){return Vector3(x*f, y*f, z*f);}float Vector3::dot(const Vector3 &v){return x*v.x + y*v.y + z*v.z;}float Vector3::length(){return sqrtf(dot(*this));}void Vector3::normalize(){float len = length();if (len < uZero) len = 1;len = 1/len;x *= len;y *= len;z *= len;}/*Cross Product叉乘公式aXb = | i,  j,  k  | | a.x a.y a.z| | b.x b.y b.z| = (a.y*b.z -a.z*b.y)i + (a.z*b.x - a.x*b.z)j + (a.x*b.y - a.y*b.x)k */Vector3 Vector3::crossProduct(const Vector3 &v){return Vector3(y * v.z - z * v.y,z * v.x - x * v.z,x * v.y - y * v.x);}void Vector3::printVec3(){std::cout<<"("<<x<<", "<<y<<", "<<z<<")"<<std::endl;}

测试主程序：

#include<iostream>#include<vector>#include"Vector3.h"using namespace std;int main() {Vector3 v31;Vector3 v32(2.0f,3.0f,4.0f);Vector3 v33(v32 - 1.0f);cout<<"We have original Vector3s:\n";v31.printVec3();v32.printVec3();v33.printVec3();cout<<"v32 crossproduct v33 is:\n";Vector3 v3233 = v32.crossProduct(v33);v3233.printVec3();cout<<"Now we normalize them:\n";v31.normalize();v32.normalize();v33.normalize();v3233.normalize();v31.printVec3();v32.printVec3();v33.printVec3();v3233.printVec3();system("pause");return 0;}

运算结果：