hdu 4998 Rotate(几何)

题目链接：hdu 4998 Rotate

题目大意：给定n次旋转，每次旋转给定旋转中心和角度，问说n次旋转的等价旋转，包括中心和角度。

解题思路：根据旋转的公式：

• x′=(x−rx)∗cos(r)−(y−ry)∗sin(r)+rx
• y′=(x−rx)∗sin(r)+(y−ry)∗cos(r)+ry
  假设起始点（0，0），经过n次旋转后得到（x',y'）然后根据公式去求x，y。

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;

const double pi = 4 * atan(1.0);

struct point {
    double x, y;
    point (double x = 0, double y = 0) {
        this->x = x;
        this->y = y;
    }
    point rotate (double rx, double ry, double r) {
        double x0 = (x - rx) * cos(r) - (y - ry) * sin(r) + rx;
        double y0 = (x - rx) * sin(r) + (y - ry) * cos(r) + ry;
        return point(x0, y0);
    }
};

int main () {
    int cas, n;
    scanf("%d", &cas);
    while (cas--) {
        double R = 0, x, y, r;
        scanf("%d", &n);

        point S;
        while (n--) {
            scanf("%lf%lf%lf", &x, &y, &r);
            R += r;

            if (R >= 2 * pi)
                R -= 2 * pi;
            S = S.rotate(x, y, r);
        }

        double a = 1 - cos(R), b = sin(R);

        double xx = (a * S.x - b * S.y) / (a * a + b * b);
        double yy = (a * S.y + b * S.x) / (a * a + b * b);
        printf("%.10lf %.10lf %.10lf\n", xx, yy, R);
    }
    return 0;
}