山东省第四届acm.Rescue The Princess(数学推导）-优快云博客

本文介绍了一个编程问题，即如何通过已知等边三角形的两个顶点坐标来计算第三个顶点坐标，以此来帮助王子找到迷宫出口并救出公主。文章提供了输入输出示例及旋转坐标系的方法。

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Rescue The Princess

Time Limit: 1 Sec Memory Limit: 128 MB Submit: 412 Solved: 168 [Submit][Status][Web Board]

Description

Several days ago, a beast caught a beautiful princess and the princess was put in prison. To rescue the princess, a prince who wanted to marry the princess set out immediately. Yet, the beast set a maze. Only if the prince find out the maze’s exit can he save the princess.

Now, here comes the problem. The maze is a dimensional plane. The beast is smart, and he hidden the princess snugly. He marked two coordinates of an equilateral triangle in the maze. The two marked coordinates are A(x1,y1) and B(x2,y2). The third coordinate C(x3,y3) is the maze’s exit. If the prince can find out the exit, he can save the princess. After the prince comes into the maze, he finds out the A(x1,y1) and B(x2,y2), but he doesn’t know where the C(x3,y3) is. The prince need your help. Can you calculate the C(x3,y3) and tell him?

Input

The first line is an integer T(1 <= T <= 100) which is the number of test cases. T test cases follow. Each test case contains two coordinates A(x1,y1) and B(x2,y2), described by four floating-point numbers x1, y1, x2, y2 ( |x1|, |y1|, |x2|, |y2| <= 1000.0).

Please notice that A(x1,y1) and B(x2,y2) and C(x3,y3) are in an anticlockwise direction from the equilateral triangle. And coordinates A(x1,y1) and B(x2,y2) are given by anticlockwise.

Output

For each test case, you should output the coordinate of C(x3,y3), the result should be rounded to 2 decimal places in a line.

Sample Input

4
-100.00 0.00 0.00 0.00
0.00 0.00 0.00 100.00
0.00 0.00 100.00 100.00
1.00 0.00 1.866 0.50

Sample Output

(-50.00,86.60)
(-86.60,50.00)
(-36.60,136.60)
(1.00,1.00)

HINT

已知一向量为(x , y) 则将它旋转θ后的坐标为（x*cosθ- y * sinθ ， y*cosθ + x * sinθ）

转载：http://www.tuicool.com/articles/FnEZJb

转载于:https://www.cnblogs.com/get-an-AC-everyday/p/4396495.html