POJ 3130 半面相交

题意：很明显判断多边形是否存在内核。

将每个边看做一个半面，判断版面是否大于2即可。

#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 n,m;
while(~scanf("%d",&n),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],g[(i+1)%n]);
hp[i].GetAngle();
}
HalfPlaneIntersect(n,m);
puts(m>2?"1":"0");
}
return 0;
}