Rescue The Princess（计算几何）

最新推荐文章于 2017-05-23 20:43:08 发布

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#计算几何

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本文介绍了一种计算已知两个顶点坐标情况下等边三角形第三个顶点坐标的算法。利用atan2函数准确确定角度，并通过三角函数计算出第三个顶点的位置。适用于计算机图形学及游戏开发中坐标计算的问题。

题意：给出一个等边三角形ABC的AB两点坐标，求C点坐标（ABC逆时针）

思路：

为什么用atan2而不用atan求角度S，见点击打开链接

代码：

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
const double pi = acos(-1.0);

int main(void)
{
    int t;
    cin >> t;
    while(t--)
    {
        double x1, x2, y1, y2;
        cin >> x1 >> y1 >> x2 >> y2;
        double l = sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));
        double s = atan2(y2-y1, x2-x1);
        printf("(%.2f,%.2f)\n", x1+l*cos(s+60.0/180*pi), y1+l*sin(s+60.0/180*pi));
    }
    return 0;
}

Rescue The Princess

Time Limit: 1000MS Memory Limit: 65536KB

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Problem 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.

Example 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

Example Output

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