多边形重心，面积

多边形面积

改革春风吹满地

#include<bits/stdc++.h>
using namespace std;
struct point
{
   double x,y;
}node[10001];
double cosr(point a,point b,point c)
{
   return (a.x-c.x)*(b.y-c.y)-(a.y-c.y)*(b.x-c.x);
}
int main( )
{
   int n;
   while(cin>>n&&n)
   {
       double sum=0;
       for(int i=0;i<n;i++)
       {
          cin>>node[i].x>>node[i].y;
       }
       for(int i=1;i<n-1;i++)
       {
          sum+=cosr(node[i],node[i+1],node[0]);
       }
       printf("%.1lf\n",sum/2.0);
   }
   return 0;
}

多边形重心

#include<bits/stdc++.h>
using namespace std;
struct tree
{
   double x,y;
} node[1000010];
double sum(tree a,tree b,tree c)
{
   return (a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y);
}
int main( )
{
   int t,n;
   cin>>t;
   while(t--)
   {
       cin>>n;
       double res=0;
       double ans=0;
       tree p;
       p.x=0;
       p.y=0;
       for(int i=0; i<n; i++)
       {
           cin>>node[i].x>>node[i].y;
       }
       for(int i=1; i<n-1; i++)
       {
           ans=sum(node[i],node[i+1],node[0]);
           res+=ans;
           p.x+=ans*(node[i].x+node[i+1].x+node[0].x)*1.0/3;
           p.y+=ans*(node[i].y+node[i+1].y+node[0].y)*1.0/3;
       }
       p.x/=res*1.0;
       p.y/=res*1.0;
       printf("%.2lf %.2lf\n",p.x,p.y);
   }

   return 0;
}