UVA 10250 题目 The Other Two Trees （计算几何）

　　类型：计算几何 （算法竞赛入门经典 P88 几何计算题）

题目：

Problem E

The Other Two Trees

Input: standard input

Output: standard output

Time Limit: 2 seconds

You have a quadrilateral shaped land whose opposite fences are of equal length. You have four neighbors whose lands are exactly adjacent to your four fences, that means you have a common fence with all of them. For example if you have a fence of length d in one side, this fence of length d is also the fence of the adjacent neighbor on that side. The adjacent neighbors have no fence in common among themselves and their lands also don’t intersect. The main difference between their land and your land is that their lands are all square shaped. All your neighbors have a tree at the center of their lands. Given the Cartesian coordinates of trees of two opposite neighbors, you will have to find the Cartesian coordinates of the other two trees.

Input

The input file contains several lines of input. Each line contains four floating point or integer numbers x1, y1, x2, y2, where (x1, y1), (x2, y2) are the coordinates of the trees of two opposite neighbors. Input is terminated by end of file.

Output

For each line of input produce one line of output which contains the line “Impossible.” without the quotes, if you cannot determine the coordinates of the other two trees. Otherwise, print four floating point numbers separated by a single space with ten digits after the decimal point ax1, ay1, ax2, ay2, where (ax1, ay1) and (ax2, ay2) are the coordinates of the other two trees. The output will be checked with special judge program, so don’t worry about the ordering of the points or small precision errors. The sample output will make it clear.

Sample Input

10 0 -10 0

10 0 -10 0

10 0 -10 0

Sample Output

0.0000000000 10.0000000000 0.0000000000 -10.0000000000

0.0000000000 10.0000000000 -0.0000000000 -10.0000000000

0.0000000000 -10.0000000000 0.0000000000 10.0000000000

1 /*
2
3 uva10250 题目： The Other Two Trees
4 题目大意： 给出正方形两个点坐标求出另外两个点的坐标
5
6
7 添平行于坐标轴的辅助线，作出全等三角形计算另外两个点的坐标
8
9 */
10
11
12
13 #include <cstdio>
14 #include <cmath>
15 using namespace std;
16
17 int main()
18 {
19
20     double x1,y1,x2,y2;
21
22     //freopen("in.txt","r",stdin);
23     while(scanf("%lf %lf %lf %lf",&x1,&y1,&x2,&y2)!=EOF)
24     {
25         double xm=0,ym=0;
26
27         xm = (x1+x2)/2;
28         ym = (y1+y2)/2;
29
30         if(x1==x2 && y1==y2)
31         {
32             printf("“Impossible.”");
33         }
34         else
35             printf("%.10f %.10f %.10f %.10f\n",xm+y1-ym,ym+xm-x1,xm+y2-ym,ym+xm-x2);
36
37     }
38
39     return 0;
40 }