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\n",cs++,X/S,Y/S);

    }

    return 0;

}

View Code