三角形ABC,坐标分别为A(x1, y1), B(x2, y2), C(x3, y3)
三角形重心坐标
x = (x1+x2+x3)/3, y = (y1+y2+y3)/3
利用行列式计算三角形面积：
三阶行列式的计算
或者用
S = （（x2-x1）*(y3-y1)-(x3-x1)*(y2-y1)）/2.0计算三角形面积
由三角形推广到n边形的重心计算公式
HUD 1115 Lifting the Stone
#include <iostream>
#include <cstdio>
using namespace std;
struct Point
{
double x, y;
};
int main()
{
int num, n, i;
Point p0, p1, p2;
double sum_x, sum_y, sum, tmp;
scanf("%d", &num);
while (num--)
{
scanf("%d", &n);
sum = sum_x = sum_y = 0.0;
scanf("%lf%lf", &p0.x, &p0.y);
scanf("%lf%lf", &p1.x, &p1.y);
for (i=2; i<n; i++)
{
scanf("%lf%lf", &p2.x, &p2.y);
tmp = ((p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y))/2.0;
sum += tmp;
sum_x += ((p0.x+p1.x+p2.x) * tmp);
sum_y += ((p0.y+p1.y+p2.y) * tmp);
p1.x = p2.x;
p1.y = p2.y;
}
printf("%.2lf %.2lf\n", sum_x/sum/3, sum_y/sum/3);
}
return 0;
}
整理地址：