hdu 3060 Area2 (计算几何模板)

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