hdu 4998

  1 #include<cstdio>
  2 #include<cmath>
  3 #include<iostream>
  4 using namespace std;
  5 
  6 struct Point{
  7     double x, y;
  8 
  9     Point(double x = 0, double y = 0): x(x), y(y){}
 10 };
 11 
 12 typedef Point Vector;
 13 
 14 const double eps = 1e-10;
 15 
 16 int dcmp(double x){
 17     if(fabs(x) < eps)
 18         return 0;
 19     return x < 0 ? -1 : 1;
 20 }
 21 
 22 bool operator == (Point A, Point B){
 23     return dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0;
 24 }
 25 
 26 Vector operator + (Vector A, Vector B){
 27     return Vector(A.x + B.x, A.y + B.y);
 28 }
 29 
 30 Vector operator - (Vector A, Vector B){
 31     return Vector(A.x - B.x, A.y - B.y);
 32 }
 33 
 34 Vector operator * (Vector A, double p){
 35     return Vector(A.x * p, A.y * p);
 36 }
 37 
 38 Vector operator / (Vector A, double p){
 39     return Vector(A.x / p, A.y / p);
 40 }
 41 
 42 double dot(Vector A, Vector B){//点乘
 43     return A.x * B.x + A.y * B.y;
 44 }
 45 
 46 double length(Vector A){//向量的模
 47     return sqrt(dot(A, A));
 48 }
 49 
 50 double angle(Vector A, Vector B){//两个向量的夹角
 51     return acos(dot(A, B) / length(A) / length(B));
 52 }
 53 
 54 Vector rotate(Vector A, double rad){//点A绕原点旋转角度为rad
 55     return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad));
 56 }
 57 
 58 Vector normal(Vector A){//向量的法向量
 59     double L = length(A);
 60     return Vector(-A.y / L, A.x / L);
 61 }
 62 
 63 double cross(Vector A, Vector B){//叉乘
 64     return A.x * B.y - A.y * B.x;
 65 }
 66 
 67 int n;
 68 Point p[11];
 69 double ra[11];
 70 
 71 void input(){
 72     cin>> n;
 73     for(int i = 0; i < n; ++i){
 74         cin>> p[i].x>> p[i].y>> ra[i];
 75         if(dcmp(ra[i] - 2 * acos(-1.0)) == 0 || dcmp(ra[i]) == 0){
 76         //当输入的弧度为0或者2π时，都是没用的
 77             ra[i] = 0;
 78             n--;
 79             i--;
 80         }
 81     }
 82 }
 83 
 84 Vector rotate_point(Vector A){//将A点绕n个点旋转
 85     for(int i = 0; i < n; ++i){
 86         A = p[i] + rotate(A - p[i], ra[i]);
 87     }
 88     return A;
 89 }
 90 
 91 Vector mid_point(Point A, Point B){//求两点之间的中点
 92     return Vector((A.x + B.x) / 2, (A.y + B.y) / 2);
 93 }
 94 
 95 Point get_line_intersection(Point P, Vector v, Point Q, Vector w){//两直线求交点，《算法入门经典训练之南》几何
 96     Vector u = P - Q;
 97     double t = cross(w, u) / cross(v, w);
 98     return P + v * t;
 99 }
100 
101 void solve(){
102     Point t1[2], t2[2], mid[2], vec[2];
103     t1[0].x = -10;
104     t1[0].y = -10;
105     t1[1].x = -100;
106     t1[1].y = -20;
107     for(int i = 0; i < 2; ++i){
108         t2[i] = rotate_point(t1[i]);
109         mid[i] = mid_point(t1[i], t2[i]);
110         vec[i] = normal(t1[i] - t2[i]);
111     }
112     Point ans = get_line_intersection(mid[0], vec[0], mid[1], vec[1]);//答案点A
113     double ansp = angle(t1[0] - ans, t2[0] - ans);//旋转角度P
114 
115     if(cross(t1[0] - ans, t2[0] - ans)  < 0){//判断是ansp 还是2π - ansp
116         ansp = 2 * acos(-1.0) - ansp;
117     }
118 
119     if(dcmp(ans.x) == 0){//加入答案是-1e-11，如果直接输出就会是-0.0000000000
120         ans.x = 0;
121     }
122     if(dcmp(ans.y) == 0){
123         ans.y = 0;
124     }
125 
126     printf("%.10lf %.10lf %.10lf\n", ans.x, ans.y, ansp);
127 }
128 
129 int main(){
130     //freopen("data.in", "r", stdin);
131     //freopen("data.out", "w", stdout);
132     int t;
133     cin>> t;
134     while(t--){
135         input();
136         solve();
137     }
138     return 0;
139 }