poj 3675 Telescope 圆和多边形的公共面积
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题目地址:poj3675
这个题和上一题是一样的。
关于求直线和圆的交点呢,可以解方程,也可以用先求出投影点,然后按照单位向量方向移动sqrt(R*R-d*d) 这么长。
先还是g++ wa,c++ ac,但是这个时候%.2lf 已经改成%.2f了
最后,干脆把所有long double 全部改成了double 这样就过了。
额,有时候double 精度又不够,wa了以后double 改成long double就过了....真是
ps,有时候想一想,是不是算得太精确也不行呢,和标程算出的结果产生误差了。
代码:
#include<iostream>#include<cmath>#include<cstdio>#include<algorithm>#include<vector>const double eps=1e-10;const double PI=acos(-1.0);using namespace std;struct Point{ double x; double y; Point(double x=0,double y=0):x(x),y(y){} void operator<<(Point &A) {cout<<A.x<<' '<<A.y<<endl;}};int dcmp(double x) {return (x>eps)-(x<-eps); }int sgn(double x) {return (x>eps)-(x<-eps); }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);}ostream &operator<<(ostream & out,Point & P) { out<<P.x<<' '<<P.y<<endl; return out;}//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;}double Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}double Cross(Vector A,Vector B) {return A.x*B.y-B.x*A.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 Area2(Point A,Point B,Point C ) {return Cross(B-A, C-A);}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(Point P,Vector v,Point Q,Vector w){ Vector u=P-Q; double t=Cross(w, u)/Cross(v,w); return P+v*t; }double DistanceToLine(Point P,Point A,Point B){ Vector v1=P-A; Vector v2=B-A; return fabs(Cross(v1,v2))/Length(v2); }double DistanceToSegment(Point P,Point A,Point B){ if(A==B) return Length(P-A); Vector v1=B-A; Vector v2=P-A; Vector v3=P-B; if(dcmp(Dot(v1,v2))==-1) return Length(v2); else if(Dot(v1,v3)>0) return Length(v3); else return DistanceToLine(P, A, B); }Point GetLineProjection(Point P,Point A,Point B){ Vector v=B-A; Vector v1=P-A; double t=Dot(v,v1)/Dot(v,v); return A+v*t;}bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){ double c1=Cross(b1-a1, a2-a1); double c2=Cross(b2-a1, a2-a1); double c3=Cross(a1-b1, b2-b1); double c4=Cross(a2-b1, b2-b1); return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0 ; }bool OnSegment(Point P,Point A,Point B){ return dcmp(Cross(P-A, P-B))==0&&dcmp(Dot(P-A,P-B))<=0;}double PolygonArea(Point *p,int n){ double area=0; for(int i=1;i<n-1;i++) { area+=Cross(p[i]-p[0], p[i+1]-p[0]); } return area/2; }Point read_point(){ Point P; scanf("%Lf%Lf",&P.x,&P.y); return P;}// ---------------与圆有关的--------struct Circle{ Point c; double r; Circle(Point c=Point(0,0),double r=0):c(c),r(r) {} Point point(double a) { return Point(c.x+r*cos(a),c.y+r*sin(a)); } };struct Line{ Point p; Vector v; Line(Point p=Point(0,0),Vector v=Vector(0,1)):p(p),v(v) {} Point point(double t) { return Point(p+v*t); } };int getLineCircleIntersection(Line L,Circle C,double &t1,double &t2,vector<Point> &sol){ double a=L.v.x; double b=L.p.x-C.c.x; double c=L.v.y; double d=L.p.y-C.c.y; double e=a*a+c*c; double f=2*(a*b+c*d); double g=b*b+d*d-C.r*C.r; double delta=f*f-4*e*g; if(dcmp(delta)<0) return 0; if(dcmp(delta)==0) { t1=t2=-f/(2*e); sol.push_back(L.point(t1)); return 1; } else { t1=(-f-sqrt(delta))/(2*e); t2=(-f+sqrt(delta))/(2*e); sol.push_back(L.point(t1)); sol.push_back(L.point(t2)); return 2; } }// 向量极角公式double angle(Vector v) {return atan2(v.y,v.x);}int getCircleCircleIntersection(Circle C1,Circle C2,vector<Point> &sol){ double d=Length(C1.c-C2.c); if(dcmp(d)==0) { if(dcmp(C1.r-C2.r)==0) return -1; // 重合 else return 0; // 内含 0 个公共点 } if(dcmp(C1.r+C2.r-d)<0) return 0; // 外离 if(dcmp(fabs(C1.r-C2.r)-d)>0) return 0; // 内含 double a=angle(C2.c-C1.c); double da=acos((C1.r*C1.r+d*d-C2.r*C2.r)/(2*C1.r*d)); Point p1=C1.point(a-da); Point p2=C1.point(a+da); sol.push_back(p1); if(p1==p2) return 1; // 相切 else { sol.push_back(p2); return 2; }}// 求点到圆的切线int getTangents(Point p,Circle C,Vector *v){ Vector u=C.c-p; double dist=Length(u); if(dcmp(dist-C.r)<0) return 0; else if(dcmp(dist-C.r)==0) { v[0]=Rotate(u,PI/2); return 1; } else { double ang=asin(C.r/dist); v[0]=Rotate(u,-ang); v[1]=Rotate(u,+ang); return 2; } }// 求两圆公切线int getTangents(Circle A,Circle B,Point *a,Point *b){ int cnt=0; if(A.r<B.r) { swap(A,B); swap(a, b); // 有时需标记 } double d=Length(A.c-B.c); double rdiff=A.r-B.r; double rsum=A.r+B.r; if(dcmp(d-rdiff)<0) return 0; // 内含 double base=angle(B.c-A.c); if(dcmp(d)==0&&dcmp(rdiff)==0) return -1 ; // 重合 无穷多条切线 if(dcmp(d-rdiff)==0) // 内切 外公切线 { a[cnt]=A.point(base); b[cnt]=B.point(base); cnt++; return 1; } // 有外公切线的情形 double ang=acos(rdiff/d); a[cnt]=A.point(base+ang); b[cnt]=B.point(base+ang); cnt++; a[cnt]=A.point(base-ang); b[cnt]=B.point(base-ang); cnt++; if(dcmp(d-rsum)==0) // 外切 有内公切线 { a[cnt]=A.point(base); b[cnt]=B.point(base+PI); cnt++; } else if(dcmp(d-rsum)>0) // 外离 又有两条外公切线 { double ang_in=acos(rsum/d); a[cnt]=A.point(base+ang_in); b[cnt]=B.point(base+ang_in+PI); cnt++; a[cnt]=A.point(base-ang_in); b[cnt]=B.point(base-ang_in+PI); cnt++; } return cnt;}Point Zero=Point(0,0);double common_area(Circle C,Point A,Point B){ // if(A==B) return 0; if(A==C.c||B==C.c) return 0; double OA=Length(A-C.c),OB=Length(B-C.c); double d=DistanceToLine(Zero, A, B); int sg=sgn(Cross(A,B)); if(sg==0) return 0; double angle=Angle(A,B); if(dcmp(OA-C.r)<=0&&dcmp(OB-C.r)<=0) { return Cross(A,B)/2; } else if(dcmp(OA-C.r)>=0&&dcmp(OB-C.r)>=0&&dcmp(d-C.r)>=0) { return sg*C.r*C.r*angle/2; } else if (dcmp(OA-C.r)>=0&&dcmp(OB-C.r)>=0&&dcmp(d-C.r)<0) { Point prj=GetLineProjection(Zero, A, B); if(OnSegment(prj, A, B)) { vector<Point> p; Line L=Line(A,B-A); double t1,t2; getLineCircleIntersection(L,C, t1, t2, p); double s1=0; s1=C.r*C.r*angle/2; double s2=0; s2=C.r*C.r*Angle(p[0],p[1])/2; s2-=fabs(Cross(p[0],p[1])/2); s1=s1-s2; return sg*s1; } else { return sg*C.r*C.r*angle/2; } } else { if(dcmp(OB-C.r)<0) { Point temp=A; A=B; B=temp; } Point inter_point; double t1,t2; Line L=Line(A,B-A); vector<Point> inter; getLineCircleIntersection(L, C, t1, t2,inter); if(OnSegment(inter[0], A, B)) inter_point=inter[0]; else { inter_point=inter[1]; } // 两种方法求交点都可以// Point prj=GetLineProjection(Zero, A, B);// // Vector v=B-A;// v=v/Length(v);// double mov=sqrt(C.r*C.r-d*d);// // if(OnSegment(prj+v*mov, A, B))// {// inter_point=prj+v*mov;// }// else// {// inter_point=prj+Vector(-v.x,-v.y)*mov;// } double s=fabs(Cross(inter_point, A)/2); s+=C.r*C.r*Angle(inter_point,B)/2; return s*sg; }}int main(){ Point p[60]; double R; int n; Circle C(Zero,0); while(cin>>R) { C.r=R; cin>>n; for(int i=0;i<n;i++) p[i]=read_point(); p[n]=p[0]; double ans=0; for(int i=0;i<n;i++) ans+=common_area(C, p[i], p[i+1]); printf("%.2f\n",fabs(ans)+eps); } return 0;}
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