Vector3——简单的3D向量类

article/2025/10/18 19:00:57

参考资料：1、 [美] 邓恩（Dunn F.）著. 3D数学基础——图形设计与开发. 史银雪，陈洪，王荣静译清华大学出版社 p57-65
2、http://www.2cto.com/kf/201311/260139.html

编程环境 QT4.8.4 + VS2010

本文用 C++实现一个简单的Vector3类的功能，已经实现的功能有：
1、重载赋值运算符“=”
2、重载“==”和“！=”操作符
3、置为零向量
4、重载一元运算符“-”
5、重载二元预算法“+”“-”
6、标量的乘除法
7、重载自反运算符
8、向量单位化
9、向量的数量积，又叫：点乘
10、向量的向量积，又加：叉乘
１１、计算两点间的距离
１２、打印向量

程序清单
1、vector3.h

#ifndef VECTOR3_H
#define VECTOR3_Hclass Vector3
{
public:float x, y, z;//构造函数//默认构造函数，初始一个零向量Vector3();//复制构造函数Vector3(const Vector3 &a);//带参数的构造函数，用三个值完成初始化Vector3(float nx, float ny, float nz);//析构函数~Vector3();//标准对象操作//重载赋值运算符，并返回引用，以实现左值。Vector3& operator=(const Vector3 &a);//重载"=="操作符bool operator==(const Vector3 &a) const ;//重载"!="操作符bool operator!=(const Vector3 &a) const ;//向量运算//置为零向量void Zero();//重载一元"-"运算符Vector3 operator-()const;//重载二元"+"和"-"运算符Vector3 operator+(const Vector3 &a) const;  Vector3 operator-(const Vector3 &a) const;  //标量的乘、除法Vector3 operator*(float a) const;Vector3 operator/(float a) const;  //重载自反运算符Vector3& operator+=(const Vector3 &a);Vector3& operator-=(const Vector3 &a);Vector3& operator*=(float a);Vector3& operator/=(float a);//向量标准化void Normalize();//向量点乘，重载标准的乘法运算符float operator*(const Vector3 &a) const;//求向量模float VectorMag(const Vector3 &a);//计算两向量的叉乘Vector3 CrossProduct(const Vector3 &a,const Vector3 &b);//计算两点间的距离float Distance (const Vector3 &a,const Vector3 &b);//打印向量void Vector3::PrintVector3();};#endif // VECTOR3_H

2、vector3.cpp

#include <iostream>
#include <qmath.h>
#include "vector3.h"//默认构造函数,初始一个零向量
Vector3::Vector3(){x=0;y=0;z=0;
}
//复制构造函数
Vector3::Vector3(const Vector3 &a){x=a.x;y=a.y;z=a.z;
}
//带参数的构造函数，用三个值完成初始化
Vector3::Vector3(float nx, float ny, float nz){x=nx;y=ny;z=nz;
}
//析构函数
Vector3::~Vector3(){};//标准对象操作
//重载赋值运算符，并返回引用，以实现左值。
Vector3& Vector3::operator=(const Vector3 &a){x =a.x;y =a.y;z =a.z;return *this;
}//重载"=="操作符
bool Vector3::operator==(const Vector3 &a) const{return x==a.x && y==a.y && z==a.z;
}//重载"!="操作符
bool Vector3::operator!=(const Vector3 &a) const{return x!=a.x || y!=a.y || z!=a.z;
}//置为零向量
void Vector3::Zero(){x = y = z = 0.0f;
}
//重载一元"-"运算符
Vector3 Vector3::operator-()const
{return Vector3(-x,-y,-z);
}//重载二元"+"和"-"运算符
Vector3 Vector3::operator+(const Vector3 &a) const{return Vector3(x+a.x,y+a.y,z+a.z);
}
Vector3 Vector3::operator-(const Vector3 &a) const{return Vector3(x-a.x,y-a.y,z-a.z);
}//标量的乘、除法
Vector3 Vector3::operator*(float a) const{return Vector3(x*a,y*a,z*a);}
Vector3 Vector3::operator/(float a) const{float oneOverA = 1.0f /a;//注意这里不对"除零"进行处理return Vector3(x*oneOverA,y*oneOverA,z*oneOverA);
}//重载自反运算符
Vector3& Vector3::operator +=(const Vector3 &a){x+=a.x;y+=a.y;z+=a.z;return *this;
}Vector3& Vector3::operator -=(const Vector3 &a){x-=a.x;y-=a.y;z-=a.z;return *this;
}
Vector3& Vector3::operator *=(float a){x *= a;y *= a;z *= a;return *this;
}
Vector3& Vector3::operator /=(float a){float oneOverA =1.0f/a;x *= oneOverA;y *= oneOverA;z *= oneOverA;return *this;
}//向量标准化
void Vector3::Normalize(){float magSq = x*x + y*y + z*z;if (magSq >0.0f){//检查除零float oneOverMag = 1.0f / sqrt(magSq);x *= oneOverMag;y *= oneOverMag;z *= oneOverMag;}
}//向量点乘，重载标准的乘法运算符
float Vector3::operator *(const Vector3 &a) const{return x*a.x + y*a.y +z *a.z;
}
void Vector3::PrintVector3(){
    std::cout <<"("<<x<<","<<y<<","<<z<<")"<<std::endl;}
//求向量模
float Vector3::VectorMag(const Vector3 &a){return sqrt(a.x * a.x + a.y * a.y + a.z * a.z);
}/* 
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  
*/  //计算两向量的叉乘
Vector3 Vector3::CrossProduct(const Vector3 &a,const Vector3 &b){return Vector3(a.y * b.z - a.z * b.y,a.z * b.x - a.x * b.z,a.x * b.y - a.y * b.x);  
}//计算两点间的距离
 float Vector3::Distance (const Vector3 &a,const Vector3 &b){float dx = a.x - b.x;float dy = a.y - b.y;float dz = a.z - b.z;return sqrt(dx * dx + dy * dy + dz * dz);
}

3、测试文件 main.cpp

#include <QtCore/QCoreApplication>
#include "vector3.h"
#include <iostream>
int main(int argc, char *argv[])
{QCoreApplication a(argc, argv);//测试构造函数Vector3 v1;Vector3 v2(3.0f,4.0f,5.0f);Vector3 v3(v2);//测试赋值运算符Vector3 v4 =v3;//打印v1.PrintVector3();v2.PrintVector3();v3.PrintVector3();v4.PrintVector3();//测试布尔运算 ==if (v1 ==v3){std::cout<<"v1=v3"<<std::endl;}else{std::cout<<"v1!=v3"<<std::endl;}if (v2 == v3){std::cout<<"v2=v3"<<std::endl;}else{std::cout<<"v2!=v3"<<std::endl;}//测试布尔运算 !=if (v1 !=v3){std::cout<<"v1!=v3"<<std::endl;}else{std::cout<<"v1=v3"<<std::endl;}if (v2 != v3){std::cout<<"v2!=v3"<<std::endl;}else{std::cout<<"v2=v3"<<std::endl;}//测试置为零向量v2.Zero();v1.PrintVector3();v2.PrintVector3();v3.PrintVector3();v4.PrintVector3();//测试一元"-"运算符Vector3 v5=-v3;v5.PrintVector3();//测试二元预算符Vector3 v_x(2.0f,3.0f,4.0f);Vector3 v_y(3.0f,3.0f,4.0f);Vector3 v_add = v_x+v_y;Vector3 v_sub = v_x-v_y;v_add.PrintVector3();v_sub.PrintVector3();//求模float mag = v2.VectorMag(v2);std::cout <<mag<<std::endl;//单位化v2.Normalize();v2.PrintVector3();return a.exec();
}