UVALive 4426 Blast the Enemy! --求多边形重心

题意：求一个不规则简单多边形的重心。

解法：多边形的重心就是所有三角形的重心对面积的加权平均数.

关于求多边形重心的文章： 求多边形重心

用叉积搞一搞就行了。

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#define Mod 1000000007
#define eps 1e-8
using namespace std;

struct Point{
    double x,y;
    Point(double x=0, double y=0):x(x),y(y) {}
    void input() { scanf("%lf%lf",&x,&y); }
};
typedef Point Vector;
int dcmp(double x) {
    if(x < -eps) return -1;
    if(x > eps) return 1;
    return 0;
}
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x*p, A.y*p); }
Vector operator / (Vector A, double p) { return Vector(A.x/p, A.y/p); }
double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }

double CalcConvexArea(Point* p,int n) {        //凸包面积
    double area = 0.0;
    for(int i=1;i<n-1;i++)
        area += Cross(p[i]-p[0],p[i+1]-p[0]);
    return area*0.5;
}
Point p[106],ch[106];

int main()
{
    int n,i,j,cs = 1;
    while(scanf("%d",&n)!=EOF && n)
    {
        for(i=0;i<n;i++) p[i].input();
        double S = CalcConvexArea(p,n);
        double X = 0.0, Y = 0.0;
        for(i=2;i<n;i++) {
            double area = 0.5*Cross(p[i-1]-p[0],p[i]-p[0]);
            X += area*(p[0].x+p[i-1].x+p[i].x)/3.0;
            Y += area*(p[0].y+p[i-1].y+p[i].y)/3.0;
        }
        printf("Stage #%d: %.6f %.6f
",cs++,X/S,Y/S);
    }
    return 0;
}