3d数学基础-旋转矩阵-C++代码实现

#include <iostream.h>
#include <math.h>
#include <assert.h>


const float kPi = 3.1415926f;
const float k2Pi = kPi*2.0f;
const float kPiover2 = kPi/2.0f;
//数学工具，计算Sin, Cos.   theta是角度
void sinCos(float* returnSin, float* returnCos, float theta)
{
*returnSin = sin(theta);
*returnCos = cos(theta);
}
//如果一个数很小，我们就把它置为0
float to_zero(float n)
{
return((abs(n)<0.00001)?0:n);
}
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)
{
//由于这是float型，有时候会出现很小的数，如果数太小，我们就用0来代替
cout<<"["<<to_zero(v.x)<<", "<<to_zero(v.y)<<", "<<to_zero(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的旋转矩阵，绕X轴旋转，绕Y轴旋转，绕Z轴旋转
class Matrix3x3
{
public:
float m11, m12, m13;
float m21, m22, m23;
float m31, m32, m33;


//axis是1时，绕X轴旋转。为2时，绕Y轴旋转。为3时，绕Z轴旋转
    void setRotate(int axis, float theta)
{
float s, c;
sinCos(&s, &c, theta);
switch(axis)
{
case 1:
m11 = 1.0f; m12 = 0.0f; m13 = 0.0f;
m21 = 0.0f; m22 = c;    m23 = s;
m31 = 0.0f; m32 = -s;   m33 = c;
break;
case 2:
m11 = c;    m12 = 0.0f; m13 = -s;
m21 = 0.0f; m22 = 1.0f; m23 = 0.0f;
m31 = s;    m32 = 0.0f; m33 = c;
break;
case 3:
m11 = c;    m12 = s;    m13 = 0.0f;
m21 = -s;    m22 = c;    m23 = 0.0f;
m31 = 0.0f;    m32 = 0.0f;    m33 = 1.0f;
break;
default:
assert(false);
}
}
};


//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<<to_zero(m.m11)<<"\t"<<to_zero(m.m12)<<"\t"<<to_zero(m.m13)<<endl;
cout<<to_zero(m.m21)<<"\t"<<to_zero(m.m22)<<"\t"<<to_zero(m.m23)<<endl;
cout<<to_zero(m.m31)<<"\t"<<to_zero(m.m32)<<"\t"<<to_zero(m.m33)<<endl;


}




int main()
{
cout<<"hello, 线性变换 - 旋转！"<<endl;
Vector3 a(10, 0, 0), b;
    Matrix3x3 M;   //M是一个旋转矩阵
M.setRotate(3, kPiover2);  //绕Z轴，旋转90度
b = a*M;   //作用旋转矩阵，将a向量变换为b向量
print_m(M);  //输出这个转换矩阵
print_v(b);


M.setRotate(3, kPi);
b = a*M;
print_v(b);
return 0;
}