ecnu1624求交集多边形面积

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本来在刷hdu的一道题。。一直没过，看到谈论区发现有凹的，我这种方法只能过凸多边形的相交面积。。

就找来这道题试下水。

两个凸多边形相交的部分要么没有 要么也是凸多边形，那就可以把这部分单独拿出来极角排序、叉积求面积。这部分的顶点要么p在q内的顶点，要么是q在p内的顶点，要么是两凸多边形的交点。

用到了点在多边形内的判定模板。

 #include <iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<stdlib.h>
 #include<vector>
 #include<cmath>
 #include<queue>
 #include<set>
 using namespace std;
 #define N 10000
 #define LL long long
 #define INF 0xfffffff
 const double eps = 1e-;
 const double pi = acos(-1.0);
 const double inf = ~0u>>;
 struct point
 {
     double x,y;
     point(double x=,double y = ):x(x),y(y) {}
 } p[N],q[N],ch[N],chh[N];
 typedef point pointt;
 point operator -(point a,point b)
 {
     return point(a.x-b.x,a.y-b.y);
 }
 int dcmp(double x)
 {
     if(fabs(x)<eps) return ;
     return x<?-:;
 }
 double cross(point a,point b)
 {
     return a.x*b.y-a.y*b.x;
 }
 double dis(point a)
 {
     return sqrt(a.x*a.x+a.y*a.y);
 }
 double getarea(point p[],int n)
 {
     int i;
     double area = ;
     for(i =  ; i < n-; i++)
         area+=cross(p[i]-p[],p[i+]-p[]);
     area = fabs(area)/;
     return area;
 }
 bool PtInPolygon (point p, point ptPolygon[], int nCount)
 {
     int i,nCross = ;
     for(i = ; i< nCount ; i++)
     {
         point p1 = ptPolygon[i];
         point p2 = ptPolygon[(i+)%nCount];
         if(dcmp(p1.y-p2.y)==) continue;
         if(dcmp(p.y-min(p1.y,p2.y))<) continue;
         if(dcmp(p.y-max(p1.y,p2.y))>=) continue;
         double x = (double)(p.y-p1.y)*(double)(p2.x-p1.x)/(double)(p2.y-p1.y)+p1.x;
         if(x>p.x)   nCross++;
     }
     return (nCross %  == );
 }
 bool segprointer(point a1,point a2,point b1,point b2)
 {
     double c1 = cross(a2-a1,b1-a1),c2 = cross(a2-a1,b2-a1);
     double c3 = cross(b2-b1,a1-b1),c4 = cross(b2-b1,a2-b1);
     return dcmp(c1)*dcmp(c2)<&&dcmp(c3)*dcmp(c4)<;
 }
 bool intersection1(point p1, point p2, point p3, point p4, point& p)      // 直线相交
 {
     double a1, b1, c1, a2, b2, c2, d;
     a1 = p1.y - p2.y;
     b1 = p2.x - p1.x;
     c1 = p1.x*p2.y - p2.x*p1.y;
     a2 = p3.y - p4.y;
     b2 = p4.x - p3.x;
     c2 = p3.x*p4.y - p4.x*p3.y;
     d = a1*b2 - a2*b1;
     if (!dcmp(d))    return false;
     p.x = (-c1*b2 + c2*b1) / d;
     p.y = (-a1*c2 + a2*c1) / d;
     return true;
 }
 double mul(point p0,point p1,point p2)
 {
     return cross(p1-p0,p2-p0);
 }

 bool cmp(point a,point b)
 {
     if(dcmp(mul(ch[],a,b))==)
         return dis(a-ch[])<dis(b-p[]);
     else
         return dcmp(mul(ch[],a,b))>;
 }
 bool cmpp(point a,point b)
 {
     if(dcmp(a.x-b.x)==) return a.y<b.y;
     return a.x<b.x;
 }
 int main()
 {
     int n,m,i,j;
     while(scanf("%d",&n)!=EOF)
     {

         for(i = ; i < n ; i++)
             scanf("%lf%lf",&p[i].x,&p[i].y);
         p[n] = p[];
         scanf("%d",&m);
         for(i = ; i < m; i++)
             scanf("%lf%lf",&q[i].x,&q[i].y);
         q[m] = q[];
         int g = ;
         for(i = ; i < n ; i ++)
         {
             if(PtInPolygon(p[i],q,m))
                 ch[g++] = p[i];
         }
         for(i = ; i < m ; i ++)
         {
             if(PtInPolygon(q[i],p,n))
                 ch[g++] = q[i];
         }
         for(i =  ; i < n;  i++)
         {
             for(j = ; j < m ; j++)
             {
                 if(segprointer(p[i],p[i+],q[j],q[j+])==) continue;
                 point pp;
                 if(!intersection1(p[i],p[i+],q[j],q[j+],pp))continue;
                 ch[g++] = pp;
             }
         }
         double ans = ;//getarea(p,n)+getarea(q,m);
         if(g==)
             ans = ;
         else
         {
             int k = ,o=;
             sort(ch,ch+g,cmpp);
             chh[o++] = ch[];
             for(i  = ; i < g; i++)
             if(dcmp(ch[i].x-ch[i-].x)==&&dcmp(ch[i].y-ch[i-].y)==)
             continue;
             else chh[o++] = ch[i];
             g = o;
             for(i = ; i < g ; i ++)
             {
                 if(dcmp(chh[i].y-chh[k].y)<||(dcmp(chh[i].y-chh[k].y)==&&dcmp(chh[i].x-chh[k].x)<))
                     k = i;
             }
             if(k!=) swap(chh[k],chh[]);
             sort(chh+,chh+g,cmp);
             ans = getarea(chh,g);
         }
         printf("%.2f\n",ans);
     }
     return ;
 }