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 once

extern 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：