圆与多边形的相交面积

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>

using namespace std;

const double eps = 1e-8;
const double PI = acos(-1.0);

int dcmp(double x){
	if( x > eps ) return 1;
	return x < -eps ? -1 : 0;
}

struct Point{
	double x,y;
	Point(){
		x = y = 0;
	}
	Point(double a,double b){
		x = a;y = b;
	}
	inline void input(){
		scanf("%lf%lf",&x,&y);
	}
	inline Point operator-(const Point &b)const{
		return Point(x - b.x,y - b.y);
	}
	inline Point operator+(const Point &b)const{
		return Point(x + b.x,y + b.y);
	}
	inline Point operator*(const double &b)const{
		return Point(x * b,y * b);
	}
	inline double dot(const Point &b)const{
		return x * b.x + y * b.y;
	}
	inline double cross(const Point &b,const Point &c)const{
		return (b.x - x) * (c.y - y) - (c.x - x) * (b.y - y);
	}
	inline double Dis(const Point &b)const{
		return sqrt((*this-b).dot(*this-b));
	}
	inline bool InLine(const Point &b,const Point &c)const{ //三点共线 
		return !dcmp(cross(b,c));
	}
	inline bool OnSeg(const Point &b,const Point &c)const{ //点在线段上，包括端点 
		return InLine(b,c) && (*this - c).dot(*this - b) < eps;
	}
};

inline double min(double a,double b){
	return a < b ? a : b;
}
inline double max(double a,double b){
	return a > b ? a : b;
}
inline double Sqr(double x){
	return x * x;
}
inline double Sqr(const Point &p){
	return p.dot(p);
}

Point LineCross(const Point &a,const Point &b,const Point &c,const Point &d){
	double u = a.cross(b,c) , v = b.cross(a,d);
	return Point((c.x * v + d.x * u) / (u + v) , (c.y * v + d.y * u) / (u + v));
} 

double LineCrossCircle(const Point &a,const Point &b,const Point &r,
                               double R,Point &p1,Point & p2){
	Point fp = LineCross(r , Point(r.x+a.y-b.y , r.y+b.x-a.x) , a , b);
	double rtol = r.Dis(fp);
	double rtos = fp.OnSeg(a , b) ? rtol : min(r.Dis(a) , r.Dis(b));
	double atob = a.Dis(b);
	double fptoe = sqrt(R * R - rtol * rtol) / atob;
	if( rtos > R - eps ) return rtos;
	p1 = fp + (a - b) * fptoe;
	p2 = fp + (b - a) * fptoe;
	return rtos;
}

double SectorArea(const Point &r,const Point &a,const Point &b,double R){ //不大于180度扇形面积，r->a->b逆时针 
	double A2 = Sqr(r - a) , B2 = Sqr(r - b) , C2 = Sqr(a - b);
	return R * R * acos( (A2 + B2 - C2) * 0.5 / sqrt(A2) / sqrt(B2)) * 0.5;
}

double TACIA(const Point &r,const Point &a,const Point &b,double R){
	double adis = r.Dis(a) , bdis = r.Dis(b);
	if( adis < R + eps && bdis < R + eps )
		return r.cross(a , b) * 0.5;
	Point ta , tb;
	if( r.InLine(a,b) ) return 0.0;
	double rtos = LineCrossCircle(a, b, r, R, ta, tb);
	if( rtos > R - eps ) 
		return SectorArea(r, a, b, R);
	if( adis < R + eps )
		return r.cross(a, tb) * 0.5 + SectorArea(r, tb, b, R);
	if( bdis < R + eps )
		return r.cross(ta, b) * 0.5 + SectorArea(r, a, ta, R);
	return r.cross(ta, tb) * 0.5 + SectorArea(r, tb, b, R) + SectorArea(r, a, ta, R);
}

const int MAXN  = 505;
Point p[MAXN];

double SPICA(int n,Point r,double R){
	int i;
	double ret = 0 , if_clock_t;
	for( i = 0 ; i < n ; ++i ){
		if_clock_t = dcmp(r.cross(p[i], p[(i + 1) % n]));
		if( if_clock_t < 0 )
			ret -= TACIA(r, p[(i + 1) % n], p[i], R);
		else ret += TACIA(r, p[i], p[(i + 1) % n], R);
	}
	return fabs(ret);
}

int main(){
	int n,i;
	scanf("%d",&n);//多边形n个顶点 
	for( i = 0 ; i < n ; ++i ) //顶点坐标 
		p[i].input();
	Point circle;
	circle.input(); //圆心坐标 
	double R;
	scanf("%lf",&R); // 圆半径 
	printf("%.10lf\n",SPICA(n,circle,R));
	return 0;
}