半平面交

存板子。

常数比较糟糕的一个板子 ，不过比较好敲

#include <bits/stdc++.h>
using namespace std;
#define DB double
const int maxn=100005;
const DB pi=acos(-1);
const DB eps=1e-6;
int n,t; DB ans;
struct N{
    DB x,y;
    N(DB a=0,DB b=0){x=a,y=b;}
}c[maxn];
struct L{
    N a,b; double f;
    L(N p=N(),N q=N()){
        a=p,b=q; f=atan2(b.y-a.y,b.x-a.x);
    }
}a[maxn],b[maxn];
N operator+(N a,N b){
    return N(a.x+b.x,a.y+b.y);
}
N operator-(N a,N b){
    return N(a.x-b.x,a.y-b.y);
}
DB operator*(N a,N b){
    return a.x*b.y-a.y*b.x;
}
DB dot(N a,N b){
    return a.x*b.x+a.y*b.y;
}
DB sqr(DB a){return a*a;}
DB dis(N a,N b){
    return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));
}
DB abs(N a){//模
    return sqrt(a.x*a.x+a.y*a.y);
}
DB COS(N a,N b){//夹角[0,pi]的cos
    return dot(a,b)/abs(a)/abs(b);
}
DB SIN(N a,N b){//夹角sin
    return fabs(a*b)/abs(a)/abs(b);
}
L go(L s,DB m){//垂直左移m
    N c=N(-sin(s.f)*m,cos(s.f)*m);
    s.a=s.a+c; s.b=s.b+c; return s;
}
bool cmpL(L a,L b){
    return fabs(a.f-b.f)>eps?a.f<b.f:(a.b-a.a)*(b.b-a.a)<-eps;//lefter
}
bool ON(N p,L e){//点在线段上
    return fabs((e.a-p)*(e.b-p))<eps
    &&(e.a.x-p.x)*(e.b.x-p.x)<eps
    &&(e.a.y-p.y)*(e.b.y-p.y)<eps;
}
N inter(L a,L b){//如果f相同,回inf或nan
    DB k1,k2,t;
    k1=(b.b-a.a)*(a.b-a.a);
    k2=(a.b-a.a)*(b.a-a.a);
    t=k1/(k1+k2);
    return N(b.b.x+(b.a.x-b.b.x)*t,b.b.y+(b.a.y-b.b.y)*t);
}
bool jud(L a,L b,L t){
    N p=inter(a,b);
    return (t.b-t.a)*(p-t.a)<eps;
}
void hpi(){
    //anticlockwise
    //保留L.a->L.b的左半平面
    sort(a+1,a+n+1,cmpL);
    t=0;
    for (int i=1;i<=n;++i)
    if (i==1||fabs(a[i].f-a[t].f)>eps) a[++t]=a[i];
    n=t;
    for (int i=1;i<n;++i)
        if (a[i+1].f-a[i].f>=pi-eps){
            if (fabs(a[i+1].f-a[i].f-pi)<eps&&(a[i+1].b-a[i].a)*(a[i].b-a[i].a)>-eps){
                printf("%.4lf
",0.0); exit(0);
            }
            puts("-1"); exit(0);
        }
    if (a[1].f+2*pi-a[n].f>=pi-eps){
        if (fabs(a[1].f+2*pi-a[n].f-pi)<eps&&(a[1].b-a[n].a)*(a[n].b-a[n].a)>-eps){
            printf("%.4lf
",0.0); exit(0);
        }
        puts("-1"); exit(0);
    }
    int l=1,r=0; t=0;
    for (int i=1;i<=n;++i)
    if (i==1||fabs(a[i].f-a[t].f)>eps) a[++t]=a[i];
    for (int i=1;i<=t;++i){
        while (l<r&&jud(b[r-1],b[r],a[i])) --r;
        while (l<r&&jud(b[l+1],b[l],a[i])) ++l;
        b[++r]=a[i];
    }
    while (l<r&&jud(b[r-1],b[r],b[l])) --r;
    while (l<r&&jud(b[l+1],b[l],b[r])) ++l;
    b[l-1]=b[r]; t=0;
    for (int i=l;i<=r;++i) c[++t]=inter(b[i-1],b[i]);
}
int main(){
    scanf("%d",&n);
    for (int i=1;i<=n;++i){
        DB A,B,C;       //Ax+By+C>=0
        scanf("%lf%lf%lf",&A,&B,&C);
        if (fabs(B)>eps){
            if (B>0) a[i]=L(N(0,-C/B),N(1,(-A-C)/B));
                else a[i]=L(N(1,(-A-C)/B),N(0,-C/B));
        }else{
            if (A>0) a[i]=L(N(-C/A,1),N(-C/A,0));
                else a[i]=L(N(-C/A,0),N(-C/A,1));
        }
    }
    hpi();
    
    ans=0;
    for (int i=2;i<t;++i) ans+=(c[i+1]-c[1])*(c[i]-c[1]);
    printf("%.4lf
",-ans/2);
    return 0;
}