计算几何 2013年山东省赛 A Rescue The Princess

题目传送门

 /*
     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）
     应用到本题，x变为(xb - xa), y变为(yb - ya)相对A点的位置，即B绕着A点旋转60度至C点
     注意：计算后加回A点的坐标才是相对于原点的坐标
     详细解释：http://www.tuicool.com/articles/FnEZJb
 */
 #include <cstdio>
 #include <cmath>
 #include <algorithm>
 #include <iostream>
 #include <cstring>
 using namespace std;

 const double PI = acos (-1.0);

 int main(void)        //A Rescue The Princess
 {
     //freopen ("A.txt", "r", stdin);

     int t;
     while (scanf ("%d", &t) == )
     {
         while (t--)
         {
             double xa, ya, xb, yb, xd, yd;
             scanf ("%lf%lf%lf%lf", &xa, &ya, &xb, &yb);
             double xc = (xb - xa) * cos (PI/3.0) - (yb - ya) * sin (PI/3.0) + xa;
             double yc = (yb - ya) * cos (PI/3.0) + (xb - xa) * sin (PI/3.0) + ya;
             printf ("(%.2f,%.2f)\n", xc, yc);
         }
     }

     return ;
 }

 /*
     分各种情况讨论，这是我比赛写的，最后因为没有去绝对值而WA几次，
     与上面的比较来看，可见好的思维和数学素养是多么重要:)
 */
 #include <cstdio>
 #include <cmath>
 #include <algorithm>
 #include <iostream>
 #include <cstring>
 using namespace std;

 int main(void)        //A Rescue The Princess
 {
     //freopen ("A.txt", "r", stdin);

     int t;
     while (scanf ("%d", &t) == )
     {
         while (t--)
         {
             double xa, ya, xb, yb, xc, yc, xd, yd;
             scanf ("%lf%lf%lf%lf", &xa, &ya, &xb, &yb);
             double ab = sqrt ((xa-xb) * (xa-xb) + (ya-yb) * (ya-yb));
             double cd = sqrt (3.0) /  * ab;
             xd = (xa + xb) / ;    yd = (ya + yb) / ;
             if (ya == yb)
             {
                 xc = (xa + xb) / ;
                 if (xa < ab)
                 {
                     yc = ya + cd;
                 }
                 else
                 {
                     yc = ya - cd;
                 }
             }
             else if (xa == xb)
             {
                 yc = (ya + yb) / ;
                 if (ya > yb)
                 {
                     xc = xa + cd;
                 }
                 else
                 {
                     xc = xa - cd;
                 }
             }
             else
             {
                 double k = (ya - yb) / (xa - xb);
                 k = -1.0 / k;
                 double q = atan (k);
                 //printf ("%.2f %.2f %.2f %.2f %.2f %.2f\n", ab, cd, xd, yd, k, q);
                 if (k > )
                 {
                     if (xa < xb)
                     {
                         xc = xd + abs (cd * cos (q));
                         yc = yd + abs (cd * sin (q));
                     }
                     else
                     {
                         xc = xd - abs (cd * cos (q));
                         yc = yd - abs (cd * sin (q));
                     }
                 }
                 else
                 {
                     if (xa < xb)
                     {
                         xc = xd - abs (cd * cos (q));
                         yc = yd + abs (cd * sin (q));
                     }
                     else
                     {
                         xc = xd + abs (cd * cos (q));
                         yc = yd - abs (cd * sin (q));
                     }
                 }
             }

             printf ("(%.2f,%.2f)\n", xc, yc);
         }
     }

     return ;
 }