Area2

4 4
0 0
0 1
1 1
1 0
0.5 0.5
0.5 1.5
1.5 1.5
1.5 0.5

1.75

给定两个多边形，求面积并

把多边形分解成三角形，然后计算三角形的有向面积交。

代码：

/* ***********************************************
Author :_rabbit
Created Time :2014/5/4 15:03:55
File Name :20.cpp
************************************************ */
#pragma comment(linker, "/STACK:102400000,102400000")
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <sstream>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <string>
#include <time.h>
#include <math.h>
#include <queue>
#include <stack>
#include <set>
#include <map>
using namespace std;
#define INF 10000000
#define eps 1e-8
#define pi acos(-1.0)
typedef long long ll;
int dcmp(double x){  
    if(fabs(x)<eps)return 0;  
    return x>0?1:-1;  
}  
struct Point{  
    double x,y;  
    Point(double _x=0,double _y=0){  
        x=_x;y=_y;  
    }  
};  
Point operator + (const Point &a,const Point &b){  
    return Point(a.x+b.x,a.y+b.y);  
}  
Point operator - (const Point &a,const Point &b){  
    return Point(a.x-b.x,a.y-b.y);  
}  
Point operator * (const Point &a,const double &p){  
    return Point(a.x*p,a.y*p);  
}  
Point operator / (const Point &a,const double &p){  
    return Point(a.x/p,a.y/p);  
}  
bool operator < (const Point &a,const Point &b){  
    return a.x<b.x||(a.x==b.x&&a.y<b.y);  
}  
bool operator == (const Point &a,const Point &b){  
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;  
}  
double Dot(Point  a,Point b){  
    return a.x*b.x+a.y*b.y;  
}  
double Length(Point a){  
    return sqrt(Dot(a,a));  
}  
double Angle(Point a,Point b){  
    return acos(Dot(a,b)/Length(a)/Length(b));  
}  
double angle(Point a){  
    return atan2(a.y,a.x);  
}  
double Cross(Point a,Point b){  
    return a.x*b.y-a.y*b.x;  
}  
Point vecunit(Point a){  
    return a/Length(a);  
}  
Point Normal(Point a){  
    return Point(-a.y,a.x)/Length(a);  
}  
Point Rotate(Point a,double rad){  
    return Point(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));  
}  
double Area2(Point a,Point b,Point c){  
    return Length(Cross(b-a,c-a));  
}  
struct Line{  
    Point p,v;  
    double ang;  
    Line(){};  
    Line(Point p,Point v):p(p),v(v){  
        ang=atan2(v.y,v.x);  
    }  
    bool operator < (const Line &L) const {  
        return ang<L.ang;  
    }  
};  
bool OnLeft(const Line &L,const Point &p){  
    return dcmp(Cross(L.v,p-L.p))>=0;  
}  
Point GetLineIntersection(Point p,Point v,Point q,Point w){  
    Point u=p-q;  
    double t=Cross(w,u)/Cross(v,w);  
    return p+v*t;  
}  
Point GetLineIntersection(Line a,Line b){  
    return GetLineIntersection(a.p,a.v,b.p,b.v);  
}  
vector<Point> HPI(vector<Line> L){  
    int n=L.size();  
    sort(L.begin(),L.end());//将所有半平面按照极角排序。  
    int first,last;  
    vector<Point> p(n);  
    vector<Line> q(n);  
    vector<Point> ans;  
    q[first=last=0]=L[0];  
    for(int i=1;i<n;i++){  
        while(first<last&&!OnLeft(L[i],p[last-1]))last--;//删除顶部的半平面  
        while(first<last&&!OnLeft(L[i],p[first]))first++;//删除底部的半平面  
        q[++last]=L[i];//将当前的半平面假如双端队列顶部。  
        if(fabs(Cross(q[last].v,q[last-1].v))<eps){//对于极角相同的，选择性保留一个。  
            last--;  
            if(OnLeft(q[last],L[i].p))q[last]=L[i];  
        }  
        if(first<last)p[last-1]=GetLineIntersection(q[last-1],q[last]);//计算队列顶部半平面交点。  
    }  
    while(first<last&&!OnLeft(q[first],p[last-1]))last--;//删除队列顶部的无用半平面。  
    //cout<<first<<" "<<last<<endl;
    if(last-first<=1)return ans;//半平面退化  
    p[last]=GetLineIntersection(q[last],q[first]);//计算队列顶部与首部的交点。  
    for(int i=first;i<=last;i++)ans.push_back(p[i]);//将队列中的点复制。  
    return ans;  
}  
double PolyArea(vector<Point> p){  
    int n=p.size();  
    double ans=0;  
    for(int i=1;i<n-1;i++)  
        ans+=Cross(p[i]-p[0],p[i+1]-p[0]);  
    return ans/2;  
}  
vector<Point> p1,p2;
int main()
{
     //freopen("data.in","r",stdin);
     //freopen("data.out","w",stdout);
     int n,m;
     while(~scanf("%d%d",&n,&m)){
         Point pp;
		 p1.clear();p2.clear();
         for(int i=0;i<n;i++)scanf("%lf%lf",&pp.x,&pp.y),p1.push_back(pp);
         for(int i=0;i<m;i++)scanf("%lf%lf",&pp.x,&pp.y),p2.push_back(pp);
         double ret1,ret2,ret=0;
         ret1=PolyArea(p1);if(dcmp(ret1)<0)reverse(p1.begin(),p1.end());ret+=fabs(ret1);
         ret2=PolyArea(p2);if(dcmp(ret2)<0)reverse(p2.begin(),p2.end());ret+=fabs(ret2);
         for(int i=1;i<n-1;i++)
             for(int j=1;j<m-1;j++){
                 vector<Point> s1,s2;
                 s1.push_back(p1[0]);
                 s1.push_back(p1[i]);
                 s1.push_back(p1[i+1]);
                 s2.push_back(p2[0]);
                 s2.push_back(p2[j]);
                 s2.push_back(p2[j+1]);
                 double r1,r2;
                 int flag1,flag2;
                 r1=PolyArea(s1);
                 if(dcmp(r1)>=0)flag1=1;else flag1=0;
                 if(dcmp(r1)<0)reverse(s1.begin(),s1.end());
                 r2=PolyArea(s2);
                 if(dcmp(r2)>=0)flag2=1;else flag2=0;
                 if(dcmp(r2)<0)reverse(s2.begin(),s2.end());
                 vector<Line> L;
                 for(int k=0;k<3;k++)
                     L.push_back(Line(s1[k],s1[(k+1)%3]-s1[k]));
                 for(int k=0;k<3;k++)
                     L.push_back(Line(s2[k],s2[(k+1)%3]-s2[k]));
                 vector<Point> tt=HPI(L);
                 if(flag1==flag2)ret-=PolyArea(tt);
                 else ret+=PolyArea(tt);
             }
         printf("%.2lf\n",ret);
     }
     return 0;
}