计算几何： 最基本的计算几何，差积 旋转

Morley's Theorem

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Description

Problem D
Morley’s Theorem
Input: Standard Input

Output: Standard Output

Morley’s theorem states that that the lines trisecting the angles of an arbitrary plane triangle meet at the vertices of an equilateral triangle. For example in the figure below the tri-sectors of angles A, B and C has intersected and created an equilateral triangle DEF.

Of course the theorem has various generalizations, in particular if all of the tri-sectZ??http://www.2cto.com/kf/ware/vc/" target="_blank" class="keylink">vcnMgYXJlIGludGVyc2VjdGVkIG9uZSBvYnRhaW5zIGZvdXIgb3RoZXIgZXF1aWxhdGVyYWwgdHJpYW5nbGVzLiBCdXQgaW4gdGhlIG9yaWdpbmFsIHRoZW9yZW0gb25seSB0cmktc2VjdG9ycyBuZWFyZXN0IHRvIEJDIGFyZSBhbGxvd2VkIHRvIGludGVyc2VjdCB0byBnZXQgcG9pbnQgRCwgdHJpLXNlY3RvcnMKIG5lYXJlc3QgdG8gQ0EgYXJlIGFsbG93ZWQgdG8gaW50ZXJzZWN0IHBvaW50IEUgYW5kIHRyaS1zZWN0b3JzIG5lYXJlc3QgdG8gQUIgYXJlIGludGVyc2VjdGVkIHRvIGdldCBwb2ludCBGLiBUcmlzZWN0b3JsaWtlIEJEIGFuZCBDRSBhcmUgbm90IGFsbG93ZWQgdG8gaW50ZXJzZWN0LiBTbyB1bHRpbWF0ZWx5IHdlIGdldCBvbmx5IG9uZSBlcXVpbGF0ZXJhbCB0cmlhbmdsZSBERUYuIE5vdyB5b3VyIHRhc2sgaXMgdG8gZmluZCB0aGUgQ2FydGVzaWFuCiBjb29yZGluYXRlcyBvZiBELCBFIGFuZCBGIGdpdmVuIHRoZSBjb29yZGluYXRlcyBvZiBBLCBCLCBhbmQgQy48L3A+CjxwPiA8L3A+CjxoNT5JbnB1dDwvaDU+CjxwPkZpcnN0IGxpbmUgb2YgdGhlIGlucHV0IGZpbGUgY29udGFpbnMgYW4gaW50ZWdlciBOICgwPE48NTAwMSkgd2hpY2ggZGVub3RlcyB0aGUgbnVtYmVyIG9mIHRlc3QgY2FzZXMgdG8gZm9sbG93LiBFYWNoIG9mIHRoZSBuZXh0IGxpbmVzIGNvbnRhaW4gc2l4IGludGVnZXJzIDxpbWcgd2lkdGg9"131" height="24" src="https://www.cppentry.com/upload_files/article/49/1_jpwbg__.gif" alt="\">. This six integers actually indicates that the Cartesian coordinates of point A, B and C are respectively. You can assume that the area of triangle ABC is not equal to zero, and the points A, B and C are in counter clockwise order.

Output

For each line of input you should produce one line of output. This line contains six floating point numbers separated by a single space. These six floating-point actually means that the Cartesian coordinates of D, E and F are respectively. Errors less than will be accepted.

Sample Input Output for Sample Input

2 

1 1 2 2 1 2 

0 0 100 0 50 50

Problemsetters: Shahriar Manzoor

Special Thanks: Joachim Wulff

Source

#include 
  
   
#include 
   
     #include 
    
      #include 
     
       #include 
      
        using namespace std; const double eps=1e-8; int dcmp(double x) { if(fabs(x)