二維向量旋轉： 二維向量旋轉代碼： [cpp] #include<iostream> #include<stdio.h> #include<math.h> using namespace std; #define N 1000 #define eps 1e-8 #define PI acos(-1.0) struct point{double x,y;}p[N]; int n; //點q繞(x0,y0) 逆時針旋轉ang point rotate(point q,double x0,double y0,double ang) { point ans; double cosa=cos(ang); double sina=sin(ang); double dx=q.x-x0; double dy=q.y-y0; ans.x=cosa*dx-sina*dy+x0; ans.y=sina*dx+cosa*dy+y0; return ans; } int main() { while(scanf("%d",&n)!=EOF) { point s={1,1}; int i; for(i=0;i<n;i++)scanf("%lf%lf",&p[i].x,&p[i].y); for(i=0;i<n;i++)p[i]=rotate(p[i],s.x,s.y,PI/4.0); for(i=0;i<n;i++)printf("%.2lf %.2lf\n",p[i].x,p[i].y); } 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 */ 三維向量旋轉： 向量繞任意軸OS(x, y, z)旋轉的矩陣： =⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢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⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥ 三維向量旋轉代碼： [cpp] #include<iostream> #include<cstdio> #include<math.h> #include<string.h> #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; //求三維空間上一點q繞 向量（x0,y0,z0）正向旋轉ang 弧度的點，向量起點在原點 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<n;i++)scanf("%lf%lf%lf",&p[i].x,&p[i].y,&p[i].z); double x0=0,y0=0,z0=1; double ang=PI/4.0; for(i=0;i<n;i++)p[i]=rotate3(p[i],x0,y0,z0,ang); for(i=0;i<n;i++)printf("%.8lf %.8lf %.8lf\n",p[i].x,p[i].y,p[i].z); } 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 */
