半平面交

存个板子

首先加限制的四条边，然后
先去平行，然后排极角序。每次加入一条边的时候，若队头两条线交点不在新半平面内，就出掉队尾。然后队头类似
最后记得去掉尾部多加的半平面。

jzoj6093

#include <cstdio>
#include <iostream>
#include <cstring>
#include <algorithm>
#include <cmath>
typedef long double ld;
using namespace std;
const int N=1e6+10;
const ld pi=acos(-1),eps=1e-14;
struct point{
	ld x,y,at;
	point operator - (const point &a){return (point){x-a.x,y-a.y};}
	point operator + (const point &a){return (point){x+a.x,y+a.y};}
	ld operator * (const point &a){return x*a.y-y*a.x;}
	point operator * (const ld a){return (point){x*a,y*a};}
	void out(){
		printf("%Lf %Lf\n",x,y);
	}
	ld len(){return x*x+y*y;}
} p[N*2];
struct line{
	point ori,vec;
	line(const point &o,const point &v){ori=o,vec=v;}
	line(){}
	bool operator < (const line &a)const{
		return vec.at < a.vec.at;
	}
} l[N*2];
int ltot;

bool cmp(const point &a,const point &b){
	return a.at < b.at;
}

int T,n;

void clearpara(){
	static line tmp[N*2];
	int g=0;
	line mx=l[1];
	for(int i=1;i<=ltot;i++){
		if(mx.vec*(l[i].ori-mx.ori)>0)mx=l[i];
		if(i==ltot||abs(l[i].vec*l[i+1].vec)>eps){
			tmp[++g]=mx;
			mx=l[i+1];
		}
	}
	ltot=g;
	memcpy(l,tmp,(g+2)*sizeof l[0]);
	for(int i=1;i<=g;i++){
		// l[i].ori.out();
		// (l[i].vec+l[i].ori).out();
		// printf("\n");
	}
}

point ict(line a,line b){
	return a.ori + a.vec * ((b.vec*(b.ori-a.ori)) / (b.vec * a.vec));
}

line Q[N*2];
point P[N*2];
ld banpm(){
	clearpara();
	int H=1,T=2;
	Q[1]=l[1],Q[2]=l[2];
	for(int i=3;i<=ltot;i++){
		while(T-H>0&&l[i].vec*(ict(Q[T],Q[T-1])-l[i].ori)<=0)T--;
		while(T-H>0&&l[i].vec*(ict(Q[H],Q[H+1])-l[i].ori)<=0)H++;
		Q[++T]=l[i];
	}
	while(T-H>0&&Q[H].vec*(ict(Q[T],Q[T-1])-Q[H].ori)<=0)T--;
	int zz;P[zz=1]=ict(Q[H],Q[T]);
	ld S=0;
	for(int i=H+1;i<=T;i++)P[++zz]=ict(Q[i-1],Q[i]);
	// for(int i=1;i<=zz;i++){
	// 	P[i].out();
	// }
	for(int i=2;i<zz;i++){
		S+=abs((P[i]-P[1]) * (P[i+1]-P[1]))/2;
	}
	return S;
}

int main(){
	freopen("everdream.in","r",stdin);
	freopen("everdream.out","w",stdout);
	cin>>T>>T;
	int c=1;
	for(;T;T--,c++){
		scanf("%d",&n);
		scanf("%Lf %Lf",&p[0].x,&p[0].y);
		for(int i=1;i<n;i++){
			scanf("%Lf %Lf",&p[i].x,&p[i].y);
			p[i]=p[i]-p[0];
			p[i].at=atan2(p[i].y,p[i].x);
		}
		// if(c==1){
		// 	cout<<n<<endl;
		// 	for(int i=0;i<n;i++)printf("%Lf %Lf\n",p[i].x,p[i].y);
		// 	return 0;
		// }
		n--;
		sort(p+1,p+1+n,cmp);
		for(int i=1;i<=n;i++)p[i+n]=p[i],p[i+n].at=p[i].at+2*pi;
		int now=1;ltot=0;
		int fl=0;
		for(int i=1;i<=n;i++){
			ld fx=p[i].at+pi;
			while(now<=2*n&&p[now].at<fx)now++;
			if(abs(p[now].at-fx)<=eps){
				fl=1;
				printf("0.0000000\n");
				break;
			}
			if(now<=2*n&&(p[now]-p[i]).len()!=0)l[++ltot]=line(p[i],p[now]-p[i]);
			if(now>1&&(p[now-1]-p[i]).len()!=0)l[++ltot]=line(p[i],p[now-1]-p[i]);
			if((p[i+1]-p[i]).len()!=0)l[++ltot]=line(p[i+1],p[i+1]-p[i]);
			if(i>1&&(p[i-1]-p[i]).len()!=0)l[++ltot]=line(p[i-1],p[i-1]-p[i]);
		}
		if(fl)continue;
		l[++ltot]=line((point){1e6,-1e6}-p[0],(point){0,2e6});
		l[++ltot]=line((point){1e6,1e6}-p[0],(point){-2e6,0});
		l[++ltot]=line((point){-1e6,1e6}-p[0],(point){0,-2e6});
		l[++ltot]=line((point){-1e6,-1e6}-p[0],(point){2e6,0});
		for(int i=1;i<=ltot;i++){
			if(l[i].vec * (l[i].ori*(-1)) <= 0){
				l[i].ori=l[i].ori + l[i].vec;
				l[i].vec=l[i].vec*(-1);
			}
			l[i].vec.at=atan2(l[i].vec.y,l[i].vec.x);
			if(pi - l[i].vec.at <= eps)
				l[i].vec.at=-pi;
		}
		sort(l+1,l+1+ltot);
		printf("%.10Lf\n",banpm());
	}
}