POJ 3675 Telescope

题意:给定一个不自交的多边形，要求和圆心在原点的圆的面积交.

思路:同POJ2986，是加强版

代码:

 #include<algorithm>
 #include<cstdio>
 #include<cmath>
 #include<cstring>
 #include<iostream>
 struct Point{
     double x,y;
     Point(){}
     Point(double x0,double y0):x(x0),y(y0){}
 }p[],a[],O;
 struct Line{
     Point s,e;
     Line(){}
     Line(Point s0,Point e0):s(s0),e(e0){}
 };
 int n;
 double R;
 const double eps=1e-;
 const double Pi=acos(-);
 double sgn(double x){
     if (x>eps) return 1.0;
     if (x<-eps) return -1.0;
     return ;
 }
 Point operator *(Point p1,double x){
     return Point(p1.x*x,p1.y*x);
 }
 Point operator /(Point p1,double x){
     return Point(p1.x/x,p1.y/x);
 }
 double operator /(Point p1,Point p2){
     return p1.x*p2.x+p1.y*p2.y;
 }
 double operator *(Point p1,Point p2){
     return p1.x*p2.y-p1.y*p2.x;
 }
 Point operator +(Point p1,Point p2){
     return Point(p1.x+p2.x,p1.y+p2.y);
 }
 Point operator -(Point p1,Point p2){
     return Point(p1.x-p2.x,p1.y-p2.y);
 }
 double dis(Point p1){
     return sqrt(p1.x*p1.x+p1.y*p1.y);
 }
 double dis(Point p1,Point p2){
     return dis(Point(p1.x-p2.x,p1.y-p2.y));
 }
 double sqr(double x){
     return x*x;
 }
 double dist_line(Line p){
     double A,B,C,dist;
     A=p.s.y-p.e.y;
     B=p.s.x-p.e.x;
     C=p.s.x*p.e.y-p.s.y*p.e.x;
     dist=fabs(C)/sqrt(sqr(A)+sqr(B));
     return dist;
 }
 double get_cos(double a,double b,double c){
     return (b*b+c*c-a*a)/(*b*c);
 }
 double get_angle(Point p1,Point p2){
     if (!sgn(dis(p1))||!sgn(dis(p2))) return 0.0;
     double A,B,C;
     A=dis(p1);
     B=dis(p2);
     C=dis(p1,p2);
     if (C<=eps) return 0.0;
     return acos(get_cos(C,A,B));
 }
 Point get_point(Point p){
     double T=sqr(p.x)+sqr(p.y);
     return Point(sgn(p.x)*sqrt(sqr(p.x)/T),sgn(p.y)*sqrt(sqr(p.y)/T));
 }
 double S(Point p1,Point p2,Point p3){
     return fabs((p2-p1)*(p3-p1))/;
 }
 double work(Point p1,Point p2){
     double f=sgn(p1*p2),res=;
     if (!sgn(f)||!sgn(dis(p1))||!sgn(dis(p2))) return 0.0;
     double l=dist_line(Line(p1,p2));
     double a=dis(p1);
     double b=dis(p2);
     double c=dis(p1,p2);
     if (a<=R&&b<=R){
         return fabs(p1*p2)/2.0*f;
     }
     if (a>=R&&b>=R&&l>=R){
         double ang=get_angle(p1,p2);
         return fabs((ang/(2.0))*(R*R))*f;
     }
     if (a>=R&&b>=R&&l<=R&&(get_cos(a,b,c)<=||get_cos(b,a,c)<=)){
         double ang=get_angle(p1,p2);
         return fabs((ang/(2.0))*(R*R))*f;
     }
     if (a>=R&&b>=R&&l<=R&&(get_cos(a,b,c)>&&get_cos(b,a,c)>)){
         double dist=dist_line(Line(p1,p2));
         double len=sqrt(sqr(R)-sqr(dist))*2.0;
         double ang1=get_angle(p1,p2);
         double cos2=get_cos(len,R,R);
         res+=fabs(len*dist/2.0);
         double ang2=ang1-acos(cos2);
         res+=fabs((ang2/())*(R*R));
         return res*f;
     }
     if ((a>=R&&b<R)||(a<R&&b>=R)){
         if (b>a) std::swap(a,b),std::swap(p1,p2);
         double T=sqr(p1.x-p2.x)+sqr(p1.y-p2.y);
         Point u=Point(sgn(p1.x-p2.x)*sqrt(sqr(p1.x-p2.x)/T),sgn(p1.y-p2.y)*sqrt(sqr(p1.y-p2.y)/T));
         double dist=dist_line(Line(p1,p2));
         double len=sqrt(R*R-dist*dist);
         double len2=sqrt(sqr(dis(p2))-sqr(dist));
         if (fabs(dis(p2+u*len2)-dist)<=eps) len+=len2;
         else len-=len2;
         Point p=p2+u*len;
         res+=S(O,p2,p);
         double ang=get_angle(p1,p);
         res+=fabs((ang/2.0)*R*R);
         return res*f;
     }
     return ;
 }
 int main(){
     O=Point(,);
     while (scanf("%lf",&R)!=EOF){
         scanf("%d",&n);
         for (int i=;i<=n;i++)
          scanf("%lf%lf",&p[i].x,&p[i].y);
         p[n+]=p[];
         double ans=;
         for (int i=;i<=n;i++)
          ans+=work(p[i],p[i+]);
         ans=fabs(ans);
         printf("%.2f\n",ans);
     }
 }