hdu 4998 矩阵表示旋转

http://acm.hdu.edu.cn/showproblem.php?pid=4998

http://blog.csdn.net/wcyoot/article/details/33310329

一个旋转变换可以转化为一个三维矩阵的变化

绕(x,y)旋转角度r，执行十次，求等价旋转点和角度

绕原点矩阵如下

由于是绕(x,y)，x1 = (x-x0)*cos0 - (y-y0)*sin0
+ x0;y1同理，那么第三行前两列即为x0*(1-cos(r)) + y0*sin(r)和y0*(1-cos(r)) - x0*sin(r)

最后根据x0*(1-cos(r))
+ y0*sin(r) = v[2][0]和y0*(1-cos(r))
- x0*sin(r) = v[2][1]列出方程即可求解等价的x0,y0

#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <string>
#include <queue>
#include <map>
#include <iostream>
#include <algorithm>
using namespace std;
#define RD(x) scanf("%d",&x)
#define RD2(x,y) scanf("%d%d",&x,&y)
#define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define clr0(x) memset(x,0,sizeof(x))
typedef long long LL;
double x,y,r;
const double pi = acos(-1.0);
struct Matrix
{
    double v[3][3];
    Matrix(){
        for(int i = 0;i < 3;++i)
            for(int j = 0;j < 3;++j)
                v[i][j] = 0;
    }
    void id(){
        for(int i = 0;i < 3;++i)
            v[i][i] = 1;
    }
    void init(){
        v[1][1] = v[0][0] = cos(r);
        v[1][0] = -(v[0][1] = sin(r));
        v[2][0] = x*(1-cos(r)) + y*sin(r);
        v[2][1] = y*(1-cos(r)) - x*sin(r);
        v[2][2] = 1;
    }
    Matrix operator * (Matrix c){
        Matrix ans;
        for(int i = 0;i < 3;++i)
            for(int j = 0;j < 3;++j)
                for(int k = 0;k < 3;++k)
                    ans.v[i][j] += v[i][k]*c.v[k][j];
        return ans;
    }
};

int main() {
	int _,n;RD(_);while(_--){
	    RD(n);
	    Matrix ans,tmp[11];
	    ans.id();
	    for(int i = 0;i < n;++i){
            scanf("%lf%lf%lf", &x, &y, &r);
            tmp[i].init();
            ans = ans*tmp[i];
	    }
        double cosr = ans.v[0][0],sinr = ans.v[0][1];
        r = atan2(sinr,cosr);
	    if(r < 0)
            r += 2*pi;
        double c1 = ans.v[2][0],c2 = ans.v[2][1];
        double y = (c2*(cosr - 1) - sinr*c1)/(-sinr*sinr-(1-cosr)*(1-cosr)),
               x = (c1*(1-cosr) - c2*sinr)/((1-cosr)*(1-cosr) + sinr*sinr);
        printf("%.10lf %.10lf %.10lf\n", x, y, r);
	}
	return 0;
}