3D数学 自定义三维向量类进行运算

3D数学 自定义向量类进行运算

设计一个3维向量类，可以实现如下运算：

零向量

负向量

向量大小、长度、模

标量与向量的乘除法

单位向量

向量的加法和减法

距离公式

向量点乘

向量叉乘

由于原理很简单，所以不解释，下面给出全部源代码：

//Vector3.h
#pragma once

class Vector3{
public:
    Vector3();
    Vector3(float X,float Y,float Z);

    //变为零向量
    void Zero();
    //求负向量
    Vector3 operator-() const;
    //求向量大小（长度或模）
    float Length() const;
    //标准化该向量
    void Normal();
    //向量的加法
    Vector3 operator+(Vector3 &rhs) const;
    Vector3& operator+=(Vector3 &rhs);
    //向量的减法
    Vector3 operator-(Vector3 &rhs) const;
    Vector3& operator-=(Vector3 &rhs);
    //向量乘标量
    Vector3 operator*(float scalar);
    //向量乘等于标量
    Vector3& operator*=(float scalar);
    //向量除以等于标量
    Vector3& operator/=(float scalar);
    //向量除以标量
    Vector3 operator/(float scalar);
    //距离公式
    float Distance(Vector3 &vec) const;
    //向量点乘
    float operator*(Vector3 &rhs) const;
    //向量叉积
    Vector3 CrossProduct(Vector3& vec) const;

public:
    float x,y,z;

};

//标量乘向量
Vector3 operator*(float scalar, Vector3& vec);

//Vector3.cpp
#include "Vector3.h"
#include <cmath>

Vector3::Vector3():x(0.0),y(0.0),z(0.0)
{

}

Vector3::Vector3(float X,float Y,float Z):x(X),y(Y),z(Z)
{

}

void Vector3::Zero()
{
    x = y = z = 0;
}

Vector3 Vector3::operator-() const
{
    return Vector3(-x,-y,-z);
}

float Vector3::Length() const
{
    return sqrt(x*x+y*y+z*z);
}

Vector3 Vector3::operator*(float scalar)
{
    return Vector3(this->x * scalar, this->y * scalar, this->z * scalar);
}

Vector3& Vector3::operator*=(float scalar)
{
    return *this = *this * scalar;
}

Vector3& Vector3::operator/=(float scalar)
{
    return *this = *this / scalar;
}

Vector3 operator*(float scalar, Vector3& vec)
{
    return vec*scalar;
}

Vector3 Vector3::operator/(float scalar)
{
    float temp = 1/ scalar;
    return *this * temp;
}

void Vector3::Normal()
{
    //计算机计算乘法的速度比除法快
    float temp = 1 / Length();
    x *= temp;
    y *= temp;
    z *= temp;
}

Vector3 Vector3::operator+(Vector3& rhs) const
{
    return Vector3(x+rhs.x,y+rhs.y,z+rhs.z);
}

Vector3& Vector3::operator+=(Vector3& rhs)
{
    *this = *this + rhs;
    return *this;
}

Vector3 Vector3::operator-(Vector3& rhs) const
{
    return Vector3(x-rhs.x,y-rhs.y,z-rhs.z);
}

Vector3& Vector3::operator-=(Vector3& rhs)
{
    *this = *this - rhs;
    return *this;
}

float Vector3::Distance(Vector3& vec) const
{
    return (*this - vec).Length();
}

float Vector3::operator*(Vector3& rhs) const
{
    return this->x * rhs.x + this->y * rhs.y + this->z * rhs.z;
}

Vector3 Vector3::CrossProduct(Vector3& vec) const
{
    return Vector3(this->y * vec.z - this->z * vec.y,
        this->z * vec.x - this->x * vec.z,
        this->x * vec.y - this->y * vec.x);
}

//main.cpp
#include "Vector3.h"
#include <iostream>
using namespace std;

void prfloatVec(Vector3 &vec)
{
    cout << "[" 
        << vec.x << "," 
        << vec.y << "," 
        << vec.z << "]" << endl;
}

int main()
{
    cout << "hello vector" << endl;

    //测试构造函数
    Vector3 v1(10,20,30);
    prfloatVec(v1);

    //测试默认拷贝构造函数
    Vector3 v2(v1);
    prfloatVec(v2);

    //测试负向量
    Vector3 v3 = -v1;
    prfloatVec(v3);

    //测试零向量
    v2.Zero();
    prfloatVec(v2);

    //测试计算向量长度
    Vector3 v4(5,-4,7);
    float r = v4.Length();
    cout << r << endl;

    //测试向量乘以标量
    Vector3 v5(-5,0,0.4f);
    Vector3 v6 = v5 * -3;
    prfloatVec(v6);

    //测试向量乘等于标量
    v5 *= -3;
    prfloatVec(v5);

    //测试向量除以标量
    Vector3 v7(4.7f,-6,8);
    Vector3 v8 = v7 / 2;
    prfloatVec(v8);

    //测试标量乘以向量
    Vector3 v9(1,2,3);
    Vector3 v10 = 2 * v9;
    prfloatVec(v10);

    //测试向量标准化
    Vector3 v11(12,-5,0);
    v11.Normal();
    prfloatVec(v11);

    //测试向量相加
    Vector3 a(1,2,3);
    Vector3 b(4,5,6);
    Vector3 r1 = a + b;
    prfloatVec(r1);

    //测试向量相减
    Vector3 r2 = b - a;
    prfloatVec(r2);

    //测试向量间距离
    Vector3 x(5,0,0);
    Vector3 y(-1,8,0);
    float d = x.Distance(y);
    cout << d << endl;

    //向量相乘
    Vector3 h1(3,-2,7);
    Vector3 h2(0,4,-1);
    float dp = h1 * h2;
    cout << dp << endl;

    //两向量间的角度
    float arc = static_cast<float>(acos(dp/(h1.Length()*h2.Length())) * 180 / 3.14149);
    cout << arc << endl;

    //两向量叉乘
    Vector3 t1(1,3,4);
    Vector3 t2(2,-5,8);
    Vector3 cp = t1.CrossProduct(t2);
    prfloatVec(cp);

    system("pause");
    return 0;

}

程序运行结果如下：

hello vector

[10,20,30]

[10,20,30]

[-10,-20,-30]

[0,0,0]

9.48683

[15,-0,-1.2]

[15,-0,-1.2]

[2.35,-3,4]

[2,4,6]

[0.923077,-0.384615,0]

[5,7,9]

[3,3,3]

10

-15

117.522

[44,0,-11]