3d数学基础—用C++实现矩阵的相乘和向理与矩阵的相乘

//计算向量的模，负向量，零向量,标量与向量的乘法,标准化向量,向量的加法和减法 ,距离公式，点乘，叉乘

#include <iostream.h>

#include <math.h>

class Vector3

{

public:

double x, y, z; //在数学上的表示 [x,y,z] ， 这里的我们定义为成员变量

public:

Vector3(){}

Vector3(const Vector3& a) : x(a.x), y(a.y), z(a.z){}

Vector3(double a, double b, double c) : x(a), y(b), z(c){}

void zero() //设置为零向量

{

x = y = z = 0;

}

Vector3 operator-() const //负向量

{

return Vector3(-x, -y, -z);

}

Vector3 operator*(float a) const //标量必须在右边

{

return Vector3(x*a, y*a, z*a);

}

Vector3 operator*=(float a) //标量必须在右边

{

x*=a; y*=a; z*=a;

return *this;

}

Vector3 operator/(float a) const //标量必须在右边

{

float oneOverA = 1.0f/a; //计算机中的除法速度比较慢

return Vector3(x*oneOverA, y*oneOverA, z*oneOverA); //目的是速度快一点

}

Vector3 operator/=(float a) //标量必须在右边

{

float oneOverA = 1.0f/a;

x*=oneOverA; y*=oneOverA; z*=oneOverA;

return *this;

}

//向量的加法，两个向量相加

Vector3 operator+(const Vector3& a) const

{

return Vector3(x+a.x, y+a.y, z+a.z);

}

//向量的减法，两个向量相减

Vector3 operator-(const Vector3& a) const

{

return Vector3(x-a.x, y-a.y, z-a.z);

}

//向量的加法，另一种方式

Vector3 operator+=(const Vector3& a)

{

x+=a.x; y+=a.y; z+=a.z;

return *this;

}

//向量的减法，另一种方式

Vector3 operator-=(const Vector3& a)

{

x-=a.x; y-=a.y; z-=a.z;

return *this;

}

//向量的标准化操作，单位向量

void normalize()

{

float magSq = x*x + y*y + z*z;

if(magSq>0.0f)

{

float oneOverMag = 1.0f/sqrt(magSq);

x *= oneOverMag;

y *= oneOverMag;

z *= oneOverMag;

}

}

//点乘

float operator*(const Vector3& a) const

{

return x*a.x + y*a.y + z*a.z;

}

};

/*

如果将数据定义为私有，需要使用友元

public:

friend Matrix3x3& operator*(const Matrix3x3& a, const Matrix3x3& b);

friend Vector3& operator*(const Vector3&p, const Matrix3x3& m);

friend void print_m(Matrix3x3 m);

//叉乘

friend Vector3 crossProduct(const Vector3& a, const Vector3& b);

friend void print_v(Vector3 v);

friend double vectorMag(const Vector3& a);

friend Vector3 operator*(float k, const Vector3& v); //定义标量的左乘

friend float distance(const Vector3& a, const Vector3& b); //两点之间的距离

*/

double vectorMag(const Vector3& a) //计算模

{

return sqrt(a.x*a.x + a.y*a.y + a.z*a.z);

}

void print_v(Vector3 v)

{

cout<<"["<<v.x<<", "<<v.y<<", "<<v.z<<"]"<<endl;

}

Vector3 operator*(float k, const Vector3& v)

{

return Vector3(k*v.x, k*v.y, k*v.z);

}

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;

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

//以上代码可以用一句代替

return vectorMag(a-b);

}

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

);

}

//一个3*3的矩阵

class Matrix3x3

{

public:

float m11, m12, m13;

float m21, m22, m23;

float m31, m32, m33;

};

//矩阵*矩阵

Matrix3x3& operator*(const Matrix3x3& a, const Matrix3x3& b)

{

Matrix3x3 r;

r.m11 = a.m11*b.m11 + a.m12*b.m21 + a.m13*b.m31;

r.m12 = a.m11*b.m12 + a.m12*b.m22 + a.m13*b.m32;

r.m13 = a.m11*b.m13 + a.m12*b.m23 + a.m13*b.m33;

r.m21 = a.m21*b.m11 + a.m22*b.m21 + a.m23*b.m31;

r.m22 = a.m21*b.m12 + a.m22*b.m22 + a.m23*b.m32;

r.m23 = a.m21*b.m13 + a.m22*b.m23 + a.m23*b.m33;

r.m31 = a.m31*b.m11 + a.m32*b.m21 + a.m33*b.m31;

r.m32 = a.m31*b.m12 + a.m32*b.m22 + a.m33*b.m32;

r.m33 = a.m31*b.m13 + a.m32*b.m23 + a.m33*b.m33;

return r;

}

//向量*矩阵

Vector3 operator*(const Vector3& p, const Matrix3x3& m)

{

return Vector3(

p.x*m.m11 + p.y*m.m21 + p.z*m.m31,

p.x*m.m12 + p.y*m.m22 + p.z*m.m32,

p.x*m.m13 + p.y*m.m23 + p.z*m.m33

);

}

//矩阵*矩阵的另一种方式

Matrix3x3& operator*=(Matrix3x3& a, const Matrix3x3& b)

{

a = a*b;

return a;

}

//向量*矩阵的另一种方式

Vector3 operator*=(Vector3& p, const Matrix3x3& m)

{

p = p*m;

return p;

}

//输出一个矩阵

void print_m(Matrix3x3 m)

{

cout<<m.m11<<"\t"<<m.m12<<"\t"<<m.m13<<endl;

cout<<m.m21<<"\t"<<m.m22<<"\t"<<m.m23<<endl;

cout<<m.m31<<"\t"<<m.m32<<"\t"<<m.m33<<endl;

}

int main()

{

cout<<"hello, 矩阵！"<<endl;

//定义两个矩阵，使这两个矩阵相乘

Matrix3x3 a, b, c;

a.m11 = 1; a.m12 = -5; a.m13 = 3;

a.m21 = 0; a.m22 = -2; a.m23 = 6;

a.m31 = 7; a.m32 = 2; a.m33 = -4;

//print_m(a);

cout<<endl<<endl;

b.m11 = -8; b.m12 = 6; b.m13 = 1;

b.m21 = 7; b.m22 = 0; b.m23 = -3;

b.m31 = 2; b.m32 = 4; b.m33 = 5;

//print_m(b);

cout<<endl<<endl;

c = a*b; //一个矩阵*另一个矩阵

print_m(c);

a*=b;

print_m(a); //一个矩阵*另一个矩阵的另一种方式

cout<<endl;

//定义一个向量和一个矩阵，使这个向量和这个矩阵相乘

Vector3 v(3,-1,4);

Matrix3x3 m;

m.m11 = -2; m.m12 = 0; m.m13 = 3;

m.m21 = 5; m.m22 = 7; m.m23 = -6;

m.m31 = 1; m.m32 = -4; m.m33 = 2;

Vector3 r;

r = v*m; //一个向量*一个矩阵

print_v(r);

v*=m; //一个向量*一个矩阵的另一种方式

print_v(v);

return 0;

}