POJ2624 4th Point【矢量加法】

4th Point

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 4943		Accepted: 1735

Description

Given are the (x,y) coordinates of the endpoints of two adjacent sides of a parallelogram. Find the (x,y) coordinates of the fourth point.

Input

Each line of input contains eight floating point numbers: the (x,y) coordinates of one of the endpoints of the first side followed by the (x,y) coordinates of the other endpoint of the first side, followed by the (x,y) coordinates of one of the endpoints of the second side followed by the (x,y) coordinates of the other endpoint of the second side. All coordinates are in meters, to the nearest mm. All coordinates are between -10000 and +10000.

Output

For each line of input, print the (x,y) coordinates of the fourth point of the parallelogram in meters, to the nearest mm, separated by a single space.

Sample Input

0.000 0.000 0.000 1.000 0.000 1.000 1.000 1.000
1.000 0.000 3.500 3.500 3.500 3.500 0.000 1.000
1.866 0.000 3.127 3.543 3.127 3.543 1.412 3.145

Sample Output

1.000 0.000
-2.500 -2.500
0.151 -0.398

问题描述：已知平行四边形的两条邻边，求第四个点的坐标

解题思路：先确定这两条边的交点，让后使用矢量和，具体看程序

AC的C++程序：

#include<iostream>
#include<cmath> 

using namespace std;

const double EPS=1e-10;

struct Point{
	double x,y;
	Point(){}
	Point(double x,double y):x(x),y(y){}
};

//矢量加 
Point operator +(Point p,Point q)
{
	return Point(p.x+q.x,p.y+q.y);
} 

//矢量减 
Point operator -(Point p,Point q)
{
	return Point(p.x-q.x,p.y-q.y);
}

//判断p和q是否为同一点 
bool IsOne(Point p,Point q)
{
	return (fabs(p.x-q.x)<EPS&&fabs(p.y-q.y)<EPS);
}

int main()
{
	Point a,b,c,d;
	while(~scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y,&c.x,&c.y,&d.x,&d.y))
	{
		Point ans;
		if(IsOne(a,c))
		{
			ans=(b-a)+(d-a)+a;
		}
		else if(IsOne(a,d))
		{
			ans=(b-a)+(c-a)+a;
		}
		else if(IsOne(b,c))
		{
			ans=(a-b)+(d-b)+b;
		}
		else if(IsOne(b,d))
		{
			ans=(a-b)+(c-d)+b;
		}
		printf("%.3lf %.3lf\n",ans.x,ans.y);
	}
	return 0;
}