Gym 100952J&&2015 HIAST Collegiate Programming Contest J. Polygons Intersection【计算几何求解两个凸多边形的相交面积板子题】

J. Polygons Intersection

time limit per test:2 seconds
memory limit per test:64 megabytes
input:standard input
output:standard output

We will not waste your time, it is a straightforward problem. Given multiple polygons, calculate the area of their intersection. For simplicity, there will be exactly 2 polygons both of them are convex, given in the counterclockwise order and have non-zero areas. Furthermore, in one polygon a vertex won't be on the sides of the other one. The figure below demonstrates the first test case.

Gym 100952J&&2015 HIAST Collegiate Programming Contest J. Polygons Intersection【计算几何求解两个凸多边形的相交面积板子题】
Input

The first line of the input will be a single integer T, the number of test cases (1  ≤  T  ≤  20). each test case contains two integers (3  ≤  N, M  ≤  40) Then a line contains N pairs of integers xi, yi (-1000  ≤  xi, yi ≤  1000) coordinates of the ith vertex of polygon A, followed by a line contains M pairs of integers xj, yj (-1000  ≤  xj, yj ≤  1000) coordinates of the jth vertex of polygon B. The coordinates are separated by a single space.

Output

For each test case, print on a single line, a single number representing the area of intersection, rounded to four decimal places.

Examples
Input
2
5 3
0 3 1 1 3 1 3 5 1 5
1 3 5 3 3 6
3 3
-1 -1 -2 -1 -1 -2
1 1 2 1 1 2
Output
2.6667
0.0000


题目链接:http://codeforces.com/gym/100952/problem/J

题意:给2个凸多边形,求相交面积

思路:板子题,学习一下!

下面给出AC代码:

  1 #include "iostream"
  2 #include "string.h"
  3 #include "stack"
  4 #include "queue"
  5 #include "string"
  6 #include "vector"
  7 #include "set"
  8 #include "map"
  9 #include "algorithm"
 10 #include "stdio.h"
 11 #include "math.h"
 12 #define ll long long
 13 #define bug(x) cout<<x<<" "<<"UUUUU"<<endl;
 14 #define mem(a) memset(a,0,sizeof(a))
 15 #define mp(x,y) make_pair(x,y)
 16 using namespace std;
 17 const long long INF = 1e18+1LL;
 18 const int inf = 1e9+1e8;
 19 const int N=1e5+100;
 20 #define maxn 510
 21 const double eps=1E-8;
 22 int sig(double d){
 23     return(d>eps)-(d<-eps);
 24 }
 25 struct Point{
 26     double x,y; Point(){}
 27     Point(double x,double y):x(x),y(y){}
 28     bool operator==(const Point&p)const{
 29         return sig(x-p.x)==0&&sig(y-p.y)==0;
 30     }
 31 };
 32 double cross(Point o,Point a,Point b){
 33     return(a.x-o.x)*(b.y-o.y)-(b.x-o.x)*(a.y-o.y);
 34 }
 35 double area(Point* ps,int n){
 36     ps[n]=ps[0];
 37     double res=0;
 38     for(int i=0;i<n;i++){
 39         res+=ps[i].x*ps[i+1].y-ps[i].y*ps[i+1].x;
 40     }
 41     return res/2.0;
 42 }
 43 int lineCross(Point a,Point b,Point c,Point d,Point&p){
 44     double s1,s2;
 45     s1=cross(a,b,c);
 46     s2=cross(a,b,d);
 47     if(sig(s1)==0&&sig(s2)==0) return 2;
 48     if(sig(s2-s1)==0) return 0;
 49     p.x=(c.x*s2-d.x*s1)/(s2-s1);
 50     p.y=(c.y*s2-d.y*s1)/(s2-s1);
 51     return 1;
 52 }
 53 //多边形切割
 54 //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
 55 //如果退化为一个点,也会返回去,此时n为1
 56 void polygon_cut(Point*p,int&n,Point a,Point b){
 57     static Point pp[maxn];
 58     int m=0;p[n]=p[0];
 59     for(int i=0;i<n;i++){
 60         if(sig(cross(a,b,p[i]))>0) pp[m++]=p[i];
 61         if(sig(cross(a,b,p[i]))!=sig(cross(a,b,p[i+1])))
 62             lineCross(a,b,p[i],p[i+1],pp[m++]);
 63     }
 64     n=0;
 65     for(int i=0;i<m;i++)
 66         if(!i||!(pp[i]==pp[i-1]))
 67             p[n++]=pp[i];
 68     while(n>1&&p[n-1]==p[0])n--;
 69 }
 70 //---------------华丽的分隔线-----------------//
 71 //返回三角形oab和三角形ocd的有向交面积,o是原点//
 72 double intersectArea(Point a,Point b,Point c,Point d){
 73     Point o(0,0);
 74     int s1=sig(cross(o,a,b));
 75     int s2=sig(cross(o,c,d));
 76     if(s1==0||s2==0)return 0.0;//退化,面积为0
 77     if(s1==-1) swap(a,b);
 78     if(s2==-1) swap(c,d);
 79     Point p[10]={o,a,b};
 80     int n=3;
 81     polygon_cut(p,n,o,c);
 82     polygon_cut(p,n,c,d);
 83     polygon_cut(p,n,d,o);
 84     double res=fabs(area(p,n));
 85     if(s1*s2==-1) res=-res;return res;
 86 }
 87 //求两多边形的交面积
 88 double intersectArea(Point*ps1,int n1,Point*ps2,int n2){
 89     if(area(ps1,n1)<0) reverse(ps1,ps1+n1);
 90     if(area(ps2,n2)<0) reverse(ps2,ps2+n2);
 91     ps1[n1]=ps1[0];
 92     ps2[n2]=ps2[0];
 93     double res=0;
 94     for(int i=0;i<n1;i++){
 95         for(int j=0;j<n2;j++){
 96             res+=intersectArea(ps1[i],ps1[i+1],ps2[j],ps2[j+1]);
 97         }
 98     }
 99     return res;//assumeresispositive!
100 }
101 //hdu-3060求两个任意简单多边形的并面积
102 Point ps1[maxn],ps2[maxn];
103 int n1,n2;
104 int main(){
105     int t;
106     cin>>t;
107     while(t--){
108         scanf("%d%d",&n1,&n2);
109         for(int i=0;i<n1;i++)
110             scanf("%lf%lf",&ps1[i].x,&ps1[i].y);
111         for(int i=0;i<n2;i++)
112             scanf("%lf%lf",&ps2[i].x,&ps2[i].y);
113         double ans=intersectArea(ps1,n1,ps2,n2);
114         //ans=fabs(area(ps1,n1))+fabs(area(ps2,n2))-ans;//容斥
115         printf("%.4f\n",ans);
116     }
117     return 0;
118 }

 

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