Euclid(几何)

http://acm.sdut.edu.cn/sdutoj/problem.php?action=showproblem&problemid=2831

题意：已知A,B,C,D,E,F的坐标，求G，H的坐标，并且已知三角形DEF的面积等于平行四边形的面积，点H在AC上。

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <iostream>
#include <string.h>
using namespace std;
struct Point
{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y) {}
};
typedef Point Vector;

Vector operator -(Point a,Point b)
{
    return Vector(a.x-b.x,a.y-b.y);
}
double Cross(Vector a,Vector b)
{
    return (a.x*b.y-a.y*b.x);
}
int main()
{
    double xa,ya,xb,yb,xc,yc,xd,yd,xe,ye,xf,yf;
    while(cin>>xa>>ya>>xb>>yb>>xc>>yc>>xd>>yd>>xe>>ye>>xf>>yf)
    {
        if (xa==0&&ya==0&&xb==0&&yb==0&&xc==0&&yc==0&&xd==0&&yd==0&&xe==0&&ye==0&&xf==0&&yf==0)
            break;
        Point A(xa,ya),B(xb,yb),C(xc,yc),D(xd,yd),E(xe,ye),F(xf,yf);
        Vector DE = E-D,DF= F-D,AB=B-A,AC=C-A;
        double S1 = fabs(Cross(DE,DF))*1/2;
        double S2 = fabs(Cross(AC,AB));
        double k = S1/S2;
        Vector AH(k*AC.x,k*AC.y);
        Point H(AH.x+xa,AH.y+ya);
        Point G(AB.x+H.x,AB.y+H.y);
        printf("%.3f %.3f %.3f %.3f
",G.x,G.y,H.x,H.y);
    }
    return 0;
}