多边形重心问题

0.000 0.000
0.500 1.000
0.500 1.000

<span style="font-size:32px;">思路：这个题，只是个公式问题，多边形面积和重心坐标问题。我昨天那个重心坐标公式错了。</span><span style="font-size:24px; font-family: Arial, Helvetica, sans-serif;">我就说一下重心坐标问题。把多边形分成若干个三角形，然后是每个三角形的</span><span style="font-size:24px;"><span style="font-family: Arial, Helvetica, sans-serif; background-color: rgb(255, 255, 255);">这个三角形的area</span><span style="font-family: Arial, Helvetica, sans-serif;">*(x的平均坐标)相加 除以总的area。</span></span>

<span style="color: rgb(51, 51, 51); font-family: arial, 宋体, sans-serif, 'Microsoft YaHei', tahoma; line-height: 23.99147605895996px; background-color: rgb(255, 102, 102);"><strong><span style="font-size:24px;">计算重心的时候，面积部分不应该带fabs。记着。。</span></strong></span>

<span style="font-size:32px;">http://zhidao.baidu.com/question/1575051969932482860#</span>

<span style="font-size:32px;">my code:</span>

<span style="font-size:18px;">#include<iostream>
#include<cmath>
#include<stdio.h>
using namespace std;
struct point
{
	double x;
	double y;
};
int main()
{
	int n,m,i;
	point a[10000];
	cin>>n;
    while(n--)
	{
	  double area=0;
	  double x1=0;
	  double y1=0;
      cin>>m;
	  for(i=0;i<m;i++)
		  cin>>a[i].x>>a[i].y;
	  for(i=0;i<=m-2;i++)
		  area+=a[i].x*a[i+1].y;
	  for(i=1;i<=m-1;i++)
		  area-=a[i].x*a[i-1].y;
	  area=area+a[m-1].x*a[0].y-a[0].x*a[m-1].y;
	  area=area/2;   
	  for(i=1;i<=m-2;i++)
		  x1+=(a[0].x+a[i].x+a[i+1].x)/3*(a[0].x*a[i].y+a[i].x*a[i+1].y+a[i+1].x*a[0].y-a[i].x*a[0].y-a[i+1].x*a[i].y-a[0].x*a[i+1].y)/2;
	  for(i=1;i<=m-2;i++)
		  y1+=(a[0].y+a[i].y+a[i+1].y)/3*(a[0].x*a[i].y+a[i].x*a[i+1].y+a[i+1].x*a[0].y-a[i].x*a[0].y-a[i+1].x*a[i].y-a[0].x*a[i+1].y)/2;
	   x1=x1/area;
	   y1=y1/area;
	   area=fabs(area);
	    if(area<0.0001)
          printf("0.000 0.000\n");
	  else
	  { printf("%.3lf ",area);
	  printf("%.3lf\n",x1+y1);}
	 }
	return 0;
}</span>

法二：pooker2008帮我改的。。哈哈

<span style="font-size:24px;">#include<iostream>
#include<cmath>
#include<stdio.h>
using namespace std;
struct point {
    double x;
    double y;
};
int main() {
    int n, m, i;
    point a[10000];
    cin >> n;
    while (n--) {
        double area = 0;
        double x1 = 0;
        double y1 = 0;
        cin >> m;
        for (i = 0; i < m; i++) {
            cin >> a[i].x >> a[i].y;
        }
        for (i = 1; i <= m - 2; i++) {
            double temp = ((a[i].x - a[0].x) * (a[i + 1].y - a[0].y) 
                         - (a[i].y - a[0].y) * (a[i + 1].x - a[0].x)) / 2.0;
            x1 += (a[0].x + a[i].x + a[i + 1].x) / 3.0 * temp;
            y1 += (a[0].y + a[i].y + a[i + 1].y) / 3.0 * temp;
            area += temp;
        }
        x1 = x1 / area;
        y1 = y1 / area;
        area = fabs(area);
        if (area < 1e-6)
            printf("0.000 0.000\n");
        else {
            printf("%.3f ", area);
            printf("%.3f\n", x1 + y1);
        }
    }
    return 0;
}</span>