POJ3675 Telescope 圆和多边形的交

POJ3675

用三角剖分可以轻松搞定，数据也小 随便AC。

#include<iostream>
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<vector>
using namespace std;
const double eps=1e-10,PI=acos(-1.0);int cmp(double k)
{return k<-eps ? -1:k>eps ? 1:0;
}const double pi=acos(-1.0);inline double sqr(double x)
{return x*x;
}struct point
{double x,y;point (){}point (double a,double b):x(a),y(b){}bool input(){return scanf("%lf%lf",&x,&y)!=EOF;}friend point operator +(const point &a,const point &b){return point(a.x+b.x,a.y+b.y);}	friend point operator -(const point &a,const point &b){return point(a.x-b.x,a.y-b.y);}friend bool operator ==(const point &a,const point &b){return cmp(a.x-b.x)==0&&cmp(a.y-b.y)==0;}friend point operator *(const point &a,const double &b){return point(a.x*b,a.y*b);}friend point operator*(const double &a,const point &b){return point(a*b.x,a*b.y);}friend point operator /(const point &a,const double &b){return point(a.x/b,a.y/b);}double norm(){return sqr(x)+sqr(y);}
};double mysqrt(double x)
{return sqrt(x);
}
double dot(const point &a,const point &b)
{return a.x*b.x+a.y*b.y;
}
double cross(const point &a,const point &b)
{return a.x*b.y-a.y*b.x;
}
double abs(const point &o)
{return sqrt(dot(o,o));
}
void circle_cross_line(point a,point b,point o,double r,point ret[],int &num)
{double x0=o.x,y0=o.y;double x1=a.x,y1=a.y;double x2=b.x,y2=b.y;double dx=x2-x1,dy=y2-y1;double A=dx*dx+dy*dy;double B=2*dx*(x1-x0)+2*dy*(y1-y0);double C=sqr(x1-x0)+sqr(y1-y0)-sqr(r);double delta=B*B-4*A*C;num=0;if(cmp(delta)>=0){double t1=(-B-mysqrt(delta))/(2*A);double t2=(-B+mysqrt(delta))/(2*A);if(cmp(t1-1)<=0&&cmp(t1)>=0){ret[num++]=point(x1+t1*dx,y1+t1*dy);}if(cmp(t2-1)<=0&&cmp(t2)>=0){ret[num++]=point(x1+t2*dx,y1+t2*dy);}}
}point crosspt(const point &a,const point &b,const point &p,const point &q)
{double a1=cross(b-a,p-a);double a2=cross(b-a,q-a);return (p*a2-q*a1)/(a2-a1);
}double sector_area(const point &a,const point &b,const double r)
{double theta=atan2(a.y,a.x)-atan2(b.y,b.x);while(cmp(theta)<=0)theta+=2*PI;while(cmp(theta-2*PI)>0)theta-=2*PI;theta=min(theta,2*PI-theta);return r*r*theta/2.;
}double calc_c(const point &a,const point &b,const double r)
{point p[2];int num=0;bool ina=cmp(abs(a)-r)<0;bool inb=cmp(abs(b)-r)<0;if(ina){if(inb)return fabs(cross(a,b))/2.;else{circle_cross_line(a,b,point(0,0),r,p,num);return fabs(sector_area(b,p[0],r))+fabs(cross(a,p[0]))/2.;}}else{if(inb){circle_cross_line(a,b,point(0,0),r,p,num);return fabs(sector_area(p[0],a,r))+fabs(cross(p[0],b))/2.;	}else{circle_cross_line(a,b,point(0,0),r,p,num);if(num==2){return fabs(sector_area(a,p[0],r))+fabs(sector_area(p[1],b,r))+fabs(cross(p[0],p[1]))/2.;}else{return fabs(sector_area(a,b,r));}}}
}double area(int n,point res[],double r)
{double ret=0.;for(int i=0;i<n;i++){int sgn=cmp(cross(res[i],res[(i+1)%n]));if(sgn!=0){ret+=sgn*calc_c(res[i],res[(i+1)%n],r);} 	}return ret;
} 
point pp[100];
int main()
{freopen("t.txt","r",stdin);double r;int n;while(scanf("%lf",&r)!=EOF){scanf("%d",&n);for(int i=0;i<n;i++)pp[i].input();pp[n]=pp[0];printf("%.2f\n",fabs(area(n,pp,r))+eps);
}return 0;
}