多边形相交面积模板

  1 /* 
  2     类型：多边形相交面积模板 
  3 */  
  4   
  5 #include<cstdio>  
  6 #include<iostream>  
  7 #include<algorithm>  
  8 #include<cstring>  
  9 #include<cmath>  
 10 using namespace std;  
 11 #define maxn 510  
 12 const double eps=1E-8;  
 13 int sig(double d){  
 14     return(d>eps)-(d<-eps);  
 15 }  
 16 struct Point{  
 17     double x,y; Point(){}  
 18     Point(double x,double y):x(x),y(y){}  
 19     bool operator==(const Point&p)const{  
 20         return sig(x-p.x)==0&&sig(y-p.y)==0;  
 21     }  
 22 };  
 23 double cross(Point o,Point a,Point b){  
 24     return(a.x-o.x)*(b.y-o.y)-(b.x-o.x)*(a.y-o.y);  
 25 }  
 26 double area(Point* ps,int n){  
 27     ps[n]=ps[0];  
 28     double res=0;  
 29     for(int i=0;i<n;i++){  
 30         res+=ps[i].x*ps[i+1].y-ps[i].y*ps[i+1].x;  
 31     }  
 32     return res/2.0;  
 33 }  
 34 int lineCross(Point a,Point b,Point c,Point d,Point&p){  
 35     double s1,s2;  
 36     s1=cross(a,b,c);  
 37     s2=cross(a,b,d);  
 38     if(sig(s1)==0&&sig(s2)==0) return 2;  
 39     if(sig(s2-s1)==0) return 0;  
 40     p.x=(c.x*s2-d.x*s1)/(s2-s1);  
 41     p.y=(c.y*s2-d.y*s1)/(s2-s1);  
 42     return 1;  
 43 }  
 44 //多边形切割  
 45 //用直线ab切割多边形p，切割后的在向量(a,b)的左侧，并原地保存切割结果  
 46 //如果退化为一个点，也会返回去,此时n为1  
 47 void polygon_cut(Point*p,int&n,Point a,Point b){  
 48     static Point pp[maxn];  
 49     int m=0;p[n]=p[0];  
 50     for(int i=0;i<n;i++){  
 51         if(sig(cross(a,b,p[i]))>0) pp[m++]=p[i];  
 52         if(sig(cross(a,b,p[i]))!=sig(cross(a,b,p[i+1])))  
 53             lineCross(a,b,p[i],p[i+1],pp[m++]);  
 54     }  
 55     n=0;  
 56     for(int i=0;i<m;i++)  
 57         if(!i||!(pp[i]==pp[i-1]))  
 58             p[n++]=pp[i];  
 59     while(n>1&&p[n-1]==p[0])n--;  
 60 }  
 61 //---------------华丽的分隔线-----------------//  
 62 //返回三角形oab和三角形ocd的有向交面积,o是原点//  
 63 double intersectArea(Point a,Point b,Point c,Point d){  
 64     Point o(0,0);  
 65     int s1=sig(cross(o,a,b));  
 66     int s2=sig(cross(o,c,d));  
 67     if(s1==0||s2==0)return 0.0;//退化，面积为0  
 68     if(s1==-1) swap(a,b);  
 69     if(s2==-1) swap(c,d);  
 70     Point p[10]={o,a,b};  
 71     int n=3;  
 72     polygon_cut(p,n,o,c);  
 73     polygon_cut(p,n,c,d);  
 74     polygon_cut(p,n,d,o);  
 75     double res=fabs(area(p,n));  
 76     if(s1*s2==-1) res=-res;return res;  
 77 }  
 78 //求两多边形的交面积  
 79 double intersectArea(Point*ps1,int n1,Point*ps2,int n2){  
 80     if(area(ps1,n1)<0) reverse(ps1,ps1+n1);  
 81     if(area(ps2,n2)<0) reverse(ps2,ps2+n2);  
 82     ps1[n1]=ps1[0];  
 83     ps2[n2]=ps2[0];  
 84     double res=0;  
 85     for(int i=0;i<n1;i++){  
 86         for(int j=0;j<n2;j++){  
 87             res+=intersectArea(ps1[i],ps1[i+1],ps2[j],ps2[j+1]);  
 88         }  
 89     }  
 90     return res;//assumeresispositive!  
 91 }  
 92 //hdu-3060求两个任意简单多边形的并面积  
 93 Point ps1[maxn],ps2[maxn];  
 94 int n1,n2;  
 95 int main(){  
 96     while(scanf("%d%d",&n1,&n2)!=EOF){  
 97         for(int i=0;i<n1;i++)  
 98             scanf("%lf%lf",&ps1[i].x,&ps1[i].y);  
 99         for(int i=0;i<n2;i++)  
100             scanf("%lf%lf",&ps2[i].x,&ps2[i].y);  
101         double ans=intersectArea(ps1,n1,ps2,n2);  
102         ans=fabs(area(ps1,n1))+fabs(area(ps2,n2))-ans;//容斥  
103         printf("%.2f
",ans);  
104     }  
105     return 0;  
106 }