3D数学向量的基础原理在计算机中的表现

C++中实现向量的编程

• 首先我们要创建一个Vector3的头文件

Vector3.h.png Vector3.png

• 接着在头文件进行Vector3的定义，以及点乘（Dot）和叉乘和各种运算符的重载

#ifndef __VECTOR3_H_INCLUDED__
#define __VECTOR3_H_INCLUDED__

#include <math.h>
class Vector3
{
public:
float x, y, z;

Vector3(){}

Vector3(const Vector3 &a) :x(a.x), y(a.y), z(a.z){}
Vector3(float nx, float ny, float nz) :x(nx), y(ny), z(nz){}

//零向量
void Zero()
{
    x = y = z = 0.0f;
}

//计算单位向量，进行标准化

void normalize()
{
    float magsq = x*x + y*y + z*z;    //平发根之前
    if (magsq > 0.0f)  //必须比0大
    {
        float temp = 1 / sqrt(magsq);
        x *= temp;
        y *= temp;
        z *= temp;

    }
}

//负向量,运算符的重载
Vector3 operator-() const { return Vector3(-x, -y, -z); }

Vector3 operator*(float a /*标量*/) const
{
    return Vector3(x*a, y*a, z*a);
}
Vector3 operator/(float a) const
{
    float temp = 1.0f / a;
    return Vector3(x*temp, y*temp, z*temp);
}

Vector3 operator*=(float a)
{
    x *= a;
    y *= a;
    z *= a;
    return *this;
}

Vector3 operator/=(float a)
{
    float temp = 1.0f / a;
    x *= temp;
    y *= temp;
    z *= temp;
    return *this;
}

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

Vector3 operator+=(const Vector3 &a)
{
    x += a.x;
    y += a.y;
    z += a.z;
    return *this;
}

Vector3 operator-=(const Vector3 &a)
{
    x -= a.x;
    y -= a.y;
    z -= a.z;
    return *this;
}

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

//点乘

float  operator*(const Vector3 &a)const
{
    return x*a.x + y*a.y + z*a.z;   
}



};

//计算向量的模
inline float vectorMag(const Vector3 &a)
{
return sqrt(a.x*a.x + a.y*a.y + a.z*a.z);
}

//非成员函数，实现向量左乘
inline Vector3 operator*(float k, const Vector3 &v)
{
return Vector3(k*v.x, k*v.y, k*v.z);
}

//计算两点之间的距离
inline float 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;

//计算向量的模。也就是大小，距离

return sqrt(dx*dx+dy*dy+dz*dz);

}

//计算叉乘

inline 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
    );
}
#endif