POJ1279(求多边形内核的面积)

题目：Art Gallery

 

先求出内核，然后再求多边形的面积就行。

/*

Goujinping 2013.4.12  NEFU

The masterplate of Polygon kernel.

Now the global variable Area stand for the area of Polygon  kernel

In most case,the problem let us judge whether the Polygon kernel
exist or not and calculate the area,perimeter,or other constants
about the Polygon kernel.

*/

#include <math.h>
#include <stdio.h>
#include <iostream>
#include <algorithm>

using namespace std;

const int N=11111;
const double EPS = 1e-8;

typedef double DIY;

DIY Area,Length;

struct Point
{
    DIY x,y;
    Point() {}
    Point(DIY _x,DIY _y):x(_x),y(_y) {}
} p[N];

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;
    DIY 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[N],q[N];

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)<EPS)
        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)))<EPS;
}

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>EPS) 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)
        p[m++]=IntersectPoint(q[i],q[i+1]);
}

void Solve(Point *p,int n,int &m)
{
    int i,j;
    Point a,b;
    p[n]=p[0];
    for(i=0;i<n;i++)
    {
        hp[i]=halfPlane(p[(i+1)%n],p[i]);
        hp[i].GetAngle();
    }
    a=p[0],b=p[1];
    HalfPlaneIntersect(n,m);

    Area=0;
    
    if(m>2)
    {
        p[m]=p[0];
        for(i=0;i<m;++i)
            Area+=CrossProduct(p[i],p[i+1]);
        if(Area<0) Area=-Area;
    }
    Area/=2.0;
}

int main()
{
    int n,m,t;
    cin>>t;
    while(t--)
    {
        cin>>n;
        for(int i=0; i<n; i++)
            cin>>p[i].x>>p[i].y;
        Solve(p,n,m);
        printf("%.2lf\n",Area);
    }
    return 0;
}