POJ 3335 半面相交

题意：给你一个多边形，问是否存在区域能看到多边形的任意位置，也就是存不存在内核。

将每条边看做一个半面求半面相交。如果存在那么半面至少三个。

#include<cmath>
#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
const int mm=111;
typedef double DIY;
struct point
{
    DIY x,y;
    point() {}
    point(DIY _x,DIY _y):x(_x),y(_y) {}
} g[mm];
point MakeVector(point &P,point &Q)
{
    return point(Q.x-P.x,Q.y-P.y);
}
DIY CrossProduct(point P,point Q)
{
    return P.x*Q.y-P.y*Q.x;
}
DIY MultiCross(point P,point Q,point R)
{
    return CrossProduct(MakeVector(Q,P),MakeVector(Q,R));
}
struct halfPlane
{
    point s,t;
    double angle;
    halfPlane() {}
    halfPlane(point _s,point _t):s(_s),t(_t) {}
    halfPlane(DIY sx,DIY sy,DIY tx,DIY ty):s(sx,sy),t(tx,ty) {}
    void GetAngle()
    {
        angle=atan2(t.y-s.y,t.x-s.x);
    }
} hp[mm],q[mm];
point IntersectPoint(halfPlane P,halfPlane Q)
{
    DIY a1=CrossProduct(MakeVector(P.s,Q.t),MakeVector(P.s,Q.s));
    DIY a2=CrossProduct(MakeVector(P.t,Q.s),MakeVector(P.t,Q.t));
    return point((P.s.x*a2+P.t.x*a1)/(a2+a1),(P.s.y*a2+P.t.y*a1)/(a2+a1));
}
bool cmp(halfPlane P,halfPlane Q)
{
    if(fabs(P.angle-Q.angle)<1e-8)
        return MultiCross(P.s,P.t,Q.s)>0;
    return P.angle<Q.angle;
}
bool IsParallel(halfPlane P,halfPlane Q)
{
    return fabs(CrossProduct(MakeVector(P.s,P.t),MakeVector(Q.s,Q.t)))<1e-8;
}
void HalfPlaneIntersect(int n,int &m)
{
    sort(hp,hp+n,cmp);
    int i,l=0,r=1;
    for(m=i=1; i<n; ++i)
        if(hp[i].angle-hp[i-1].angle>1e-8)hp[m++]=hp[i];
    n=m;
    m=0;
    q[0]=hp[0],q[1]=hp[1];
    for(i=2; i<n; ++i)
    {
        if(IsParallel(q[r],q[r-1])||IsParallel(q[l],q[l+1]))return;
        while(l<r&&MultiCross(hp[i].s,hp[i].t,IntersectPoint(q[r],q[r-1]))>0)--r;
        while(l<r&&MultiCross(hp[i].s,hp[i].t,IntersectPoint(q[l],q[l+1]))>0)++l;
        q[++r]=hp[i];
    }
    while(l<r&&MultiCross(q[l].s,q[l].t,IntersectPoint(q[r],q[r-1]))>0)--r;
    while(l<r&&MultiCross(q[r].s,q[r].t,IntersectPoint(q[l],q[l+1]))>0)++l;
    q[++r]=q[l];
    for(i=l; i<r; ++i)
        g[m++]=IntersectPoint(q[i],q[i+1]);
}
int main()
{
    int t,n,m;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        for(int i=0; i<n; i++)
            scanf("%lf%lf",&g[i].x,&g[i].y);
        for(int i=0; i<n; i++)
        {
            hp[i]=halfPlane(g[(i+1)%n],g[i]);
            hp[i].GetAngle();
        }
        HalfPlaneIntersect(n,m);
        puts(m>2?"YES":"NO");
    }
    return 0;
}