二维和三维向量的旋转

}

return 0;

}

/*

in:

4

1 1

2 0

3 1

2 2

out:

1.00 1.00

2.41 1.00

2.41 2.41

1.00 2.41

*/

三维向量旋转：

向量绕任意轴OS(x, y, z)旋转的矩阵：

= x2+(y2+z2)cosθx2+y2+z2yx(1 cosθ)x2+y2+z2+zsinθx2+y2+z2 √zx(1 cosθ)x2+y2+z2 ysinθx2+y2+z2 √xy(1 cosθ)x2+y2+z2 zsinθx2+y2+z2 √y2+(z2+x2)cosθx2+y2+z2zy(1 cosθ)x2+y2+z2+xsinθx2+y2+z2 √xz(1 cosθ)x2+y2+z2+ysinθx2+y2+z2 √yz(1 cosθ)x2+y2+z2 xsinθx2+y2+z2 √z2+(x2+y2)cosθx2+y2+z2

三维向量旋转代码：

[cpp]

#include

#include

#include

#include

#define PI acos(-1.0)

#define eps 1e-8

#define N 1000

using namespace std;

struct point3{double x,y,z;}p[N];

int n;

//求三维空间上一点q绕 向量（x0,y0,z0）正向旋转ang 弧度的点，向量起点在原点

point3 rotate3(point3 q,double x0,double y0,double z0,double ang)

{

double x2=x0*x0;

double y2=y0*y0;

double z2=z0*z0;

double d2=x2+y2+z2;

double d=sqrt(d2);

double sina=sin(ang);

double cosa=cos(ang);

point3 ans;

ans.x=(x2+(y2+z2)*cosa)/d2*q.x

+ (x0*y0*(1-cosa)/d2 - z0*sina/d )* q.y

+ (x0*z0*(1-cosa)/d2+y0*sina/d)*q.z;

ans.y=(y0*x0*(1-cosa)/d2+z0*sina/d)*q.x

+ (y2+(x2+z2)*cosa)/d2* q.y

+ (y0*z0*(1-cosa)/d2-x0*sina/d)*q.z;

ans.z=(z0*x0*(1-cosa)/d2 - y0*sina/d)*q.x

+ (z0*y0*(1-cosa)/d2+x0*sina/d)*q.y

+ (z2+(x2+y2)*cosa)/d2*q.z;

return ans;

}

int main()

{

#ifndef Online_Judge

freopen("in.txt","r",stdin);

#endif

while(scanf("%d",&n)!=EOF)

{

int i;

for(i=0;i

double x0=0,y0=0,z0=1;

double ang=PI/4.0;

for(i=0;i

for(i=0;i

}

return 0;

}

/*

in:

8

0 0 0

1 -1 0

2 0 0

1 1 0

0 0 1

1 -1 1

2 0 1

1 1 1

out:

0.00000000 0.00000000 0.00000000

1.41421356 -0.00000000 0.00000000

1.41421356 1.41421356 0.00000000

0.00000000 1.41421356 0.00000000

0.00000000 0.00000000 1.00000000

1.41421356 -0.00000000 1.00000000

1.41421356 1.41421356 1.00000000

0.00000000 1.41421356 1.00000000

*/