一开始的时候有一个坐标系（正常的），然后有n个操作，每个操作是 x y d,意思是当前坐标系围绕x,y点逆时针旋转d度，最后让你输出三个数x y d，把这n个操作的最后结果，用一步等效过来，就是找到一个点，逆时针旋转一个度数，等于当前的这个状态。
思路：
我们可以用一个向量来代表当前坐标系，每次操作把当前向量拆成两个点单独操作，假如当前向量a,b，绕点c旋转d度，那么我们可以等效向量c,a逆时针旋转d，然后向量c,b逆时针旋转d，这样就的到了两个新的向量，此时我们要根据这两个新的向量求出当前这两个点的新位置，然后再用当前的新位置和下一组操作，最后得到了最终的一个向量，现在我们只要求出初始向量和最终向量的转换关系就行了，这个地方首先我们求转换点，求法是两个向量的x，x'连线，y.y'连线，两条线段中垂线的交点，求出交点之后再用余弦定理求出夹角，然后在用向量的关系来判断要不要用2PI-当前度数，具体看代码。
#include<math.h> #include<algorithm> #include<stdio.h> #define maxn 60 #define eps 1e-7 #define PP (3.141592653589793238) using namespace std; int dcmp(double x) { if(fabs(x)<eps) return 0; else return x<0?-1:1; } double toRad(double deg) { return deg/180.0*acos(-1.0); } struct Point { double x,y; Point(){} Point(double x,double y):x(x),y(y) {} void input() { scanf("%lf %lf",&x,&y); } }; typedef Point Vector; Vector operator+( Vector A, Vector B ) { return Vector( A.x + B.x, A.y + B.y ); } Vector operator-(Vector A,Vector B) { return Vector( A.x - B.x, A.y - B.y ); } Vector operator*( Vector A, double p ) { return Vector( A.x * p, A.y * p ); } Vector operator/( Vector A, double p ) { return Vector( A.x / p, A.y / p ); } bool operator<(const Point& A, const Point& B ) { return dcmp( A.x - B.x ) < 0 || ( dcmp( A.x - B.x ) == 0 && dcmp( A.y - B.y ) < 0 ); } bool operator==( const Point& a, const Point& b ) { return dcmp( a.x - b.x ) == 0 && dcmp( a.y - b.y ) == 0; } struct Line { Point s,e; Vector v; Line() {} Line(Point s,Point v,int type): s(s),v(v){} Line(Point s,Point e):s(s),e(e) {v=e-s;} }; double Dot(Vector A,Vector B) { return A.x*B.x+A.y*B.y; } double Length(Vector A) { return sqrt(Dot(A,A)); } double Angle(Vector A,Vector B) { return acos(Dot(A,B)/Length(A)/Length(B)); } double Cross(Vector A,Vector B) { return A.x*B.y-A.y*B.x; } double Area2(Point A,Point B,Point C ) { return Cross(B-A,C-A); } double Dist(Point A,Point B) { return Length(A-B); } Vector Rotate(Vector A, double rad) { return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad)); } Vector Normal(Vector A) { double L=Length(A); return Vector(-A.y/L,A.x/L); } Point GetLineIntersection(Line l1,Line l2) { Point P=l1.s; Vector v=l1.v; Point Q=l2.s; Vector w=l2.v; Vector u=P-Q; double t=Cross(w,u)/Cross(v,w); return P+v*t; } double DistanceToLine(Point P,Line L) { Point A,B; A=L.s,B=L.e; Vector v1=B-A,v2=P-A; return fabs(Cross(v1,v2))/Length(v1); } double DistanceToSegment(Point P, Line L) { Point A,B; A=L.s,B=L.e; if(A==B) return Length(P-A); Vector v1=B-A,v2=P-A,v3=P-B; if (dcmp(Dot(v1,v2))<0) return Length(v2); else if (dcmp(Dot(v1,v3))>0) return Length(v3); else return fabs(Cross(v1,v2)) / Length(v1); } Point GetLineProjection(Point P,Line L) { Point A,B; A=L.s,B=L.e; Vector v=B-A; return A+v*(Dot(v,P-A)/Dot(v,v)); } double abss(double x) { return x < 0 ? -x : x; } bool OnSegment(Point p,Line l) { Point a1=l.s; Point a2=l.e; return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dist(p,a1)+Dist(p,a2)-Dist(a1,a2))==0; } bool Paralled(Line l1,Line l2) { return dcmp(Cross(l1.e-l1.s,l2.e-l2.s))==0; } bool SegmentProperIntersection(Line l1,Line l2) { if(Paralled(l1,l2)) { return false; } Point t=GetLineIntersection(l1,l2); if(OnSegment(t,l1)) { return true; } return false; } int main () { double x ,y ,p; int T ,n ,i; scanf("%d" ,&T); while(T--) { scanf("%d" ,&n); double nowx1 = 0 ,nowy1 = 0; double nowx2 = 0 ,nowy2 = 101.0; double sss = 0;; Vector A ,B; for(i = 1 ;i <= n ;i ++) { scanf("%lf %lf %lf" ,&x ,&y ,&p); if(p == 0.0 || abss(p - PP * 2) <= 0.00001) continue; sss += p; A.x = nowx1 - x ,A.y = nowy1 - y; B = Rotate(A ,p); nowx1 = x + B.x ,nowy1 = y + B.y; A.x = nowx2 - x ,A.y = nowy2 - y; B = Rotate(A ,p); nowx2 = x + B.x ,nowy2 = y + B.y; } if(nowx1 == 0.0 && nowy1 == 0.0) { double x4 = nowx2 ,y4 = nowy2; double x3 = 0 ,y3 = 0; double x1 = 0 ,y1 = 101.0; double aaa; double tmp = (x4 - x3) * (x1 - x3) + (y4 - y3) * (y1 - y3); tmp = tmp / (pow(x4 - x3 ,2.0) + pow(y4 - y3 ,2.0)); aaa = acos(tmp); double q1 = 0 ,q2 = 0; if(nowx2 > 0.0) aaa = PP * 2 - aaa; if(abss(aaa - PP * 2) <= 0.00001)aaa = 0; printf("%lf %lf %lf " ,q1 ,q2 ,aaa); } else if(nowx2 == 0.0 && nowy2 == 101.0) { double x4 = nowx1 ,y4 = nowy1; double x3 = 0 ,y3 = 101.0; double x1 = 0 ,y1 = 0; double aaa; double tmp = (x4 - x3) * (x1 - x3) + (y4 - y3) * (y1 - y3); tmp = tmp / (pow(x4 - x3 ,2.0) + pow(y4 - y3 ,2.0)); aaa = acos(tmp); double q1 = 0 ,q2 = 101.0; if(nowx1 < 0) aaa = PP * 2 - aaa; if(abss(aaa - PP * 2) <= 0.00001)aaa = 0; printf("%lf %lf %lf " ,q1 ,q2 ,aaa); } else { Point AA1; AA1.x = AA1.y = 0; Point BB1; BB1.x = nowx1 ,BB1.y = nowy1; Line now1 = Line((AA1 + BB1)/2 ,Normal(AA1 - BB1),1); Point AA2; AA2.x = 0 ,AA2.y = 101.0; Point BB2; BB2.x = nowx2 ,BB2.y = nowy2; Line now2 = Line((AA2 + BB2)/2 ,Normal(AA2 - BB2),1); Point now = GetLineIntersection(now1 ,now2); double x4 = nowx1 ,y4 = nowy1; double x3 = now.x ,y3 = now.y; double x1 = 0 ,y1 = 0; double aaa; double tmp = (x4 - x3) * (x1 - x3) + (y4 - y3) * (y1 - y3); tmp = tmp / (pow(x4 - x3 ,2.0) + pow(y4 - y3 ,2.0)); double x2 ,y2; x1 = 0 ,y1 = 101; x2 = nowx2 - nowx1 ,y2 = nowy2 - nowy1; aaa = acos(tmp); if(x1*y2-x2*y1<0) aaa = PP * 2 - aaa; printf("%lf %lf %lf " ,now.x ,now.y ,aaa); } } return 0; }