// This file was automatically generated by sectors.cpp
// This file is part of ephi (http://www.mare.ee/indrek/ephi/)

#include "math3d.hpp"

// 3x3 transformation matrixes, forward and backwards
static transf3d_pair transforms[48] = {
  {transf3d(1, 0, 0, 0, 0, 1, 0, 1, 0), transf3d(1, 0, 0, 0, 0, 1, 0, 1, 0)},
  {transf3d(-1, 0, 0, 0, 0, 1, 0, 1, 0), transf3d(-1, 0, 0, 0, 0, 1, 0, 1, 0)},
  {transf3d(0, 1, 0, 0, 0, 1, 1, 0, 0), transf3d(0, 0, 1, 1, 0, 0, 0, 1, 0)},
  {transf3d(0, -1, 0, 0, 0, 1, 1, 0, 0), transf3d(0, 0, 1, -1, 0, 0, 0, 1, 0)},
  {transf3d(0, 0, 1, 0, 1, 0, 1, 0, 0), transf3d(0, 0, 1, 0, 1, 0, 1, 0, 0)},
  {transf3d(0, 0, -1, 0, 1, 0, 1, 0, 0), transf3d(0, 0, 1, 0, 1, 0, -1, 0, 0)},
  {transf3d(1, 0, 0, 0, 1, 0, 0, 0, 1), transf3d(1, 0, 0, 0, 1, 0, 0, 0, 1)},
  {transf3d(-1, 0, 0, 0, 1, 0, 0, 0, 1), transf3d(-1, 0, 0, 0, 1, 0, 0, 0, 1)},
  {transf3d(0, 1, 0, 1, 0, 0, 0, 0, 1), transf3d(0, 1, 0, 1, 0, 0, 0, 0, 1)},
  {transf3d(0, -1, 0, 1, 0, 0, 0, 0, 1), transf3d(0, 1, 0, -1, 0, 0, 0, 0, 1)},
  {transf3d(0, 0, 1, 1, 0, 0, 0, 1, 0), transf3d(0, 1, 0, 0, 0, 1, 1, 0, 0)},
  {transf3d(0, 0, -1, 1, 0, 0, 0, 1, 0), transf3d(0, 1, 0, 0, 0, 1, -1, 0, 0)},
  {transf3d(1, 0, 0, 0, -1, 0, 0, 0, 1), transf3d(1, 0, 0, 0, -1, 0, 0, 0, 1)},
  {transf3d(-1, 0, 0, 0, -1, 0, 0, 0, 1), transf3d(-1, 0, 0, 0, -1, 0, 0, 0, 1)},
  {transf3d(0, 1, 0, -1, 0, 0, 0, 0, 1), transf3d(0, -1, 0, 1, 0, 0, 0, 0, 1)},
  {transf3d(0, -1, 0, -1, 0, 0, 0, 0, 1), transf3d(0, -1, 0, -1, 0, 0, 0, 0, 1)},
  {transf3d(0, 0, 1, -1, 0, 0, 0, 1, 0), transf3d(0, -1, 0, 0, 0, 1, 1, 0, 0)},
  {transf3d(0, 0, -1, -1, 0, 0, 0, 1, 0), transf3d(0, -1, 0, 0, 0, 1, -1, 0, 0)},
  {transf3d(1, 0, 0, 0, 0, 1, 0, -1, 0), transf3d(1, 0, 0, 0, 0, -1, 0, 1, 0)},
  {transf3d(-1, 0, 0, 0, 0, 1, 0, -1, 0), transf3d(-1, 0, 0, 0, 0, -1, 0, 1, 0)},
  {transf3d(0, 1, 0, 0, 0, 1, -1, 0, 0), transf3d(0, 0, -1, 1, 0, 0, 0, 1, 0)},
  {transf3d(0, -1, 0, 0, 0, 1, -1, 0, 0), transf3d(0, 0, -1, -1, 0, 0, 0, 1, 0)},
  {transf3d(0, 0, 1, 0, 1, 0, -1, 0, 0), transf3d(0, 0, -1, 0, 1, 0, 1, 0, 0)},
  {transf3d(0, 0, -1, 0, 1, 0, -1, 0, 0), transf3d(0, 0, -1, 0, 1, 0, -1, 0, 0)},
  {transf3d(1, 0, 0, 0, 0, -1, 0, -1, 0), transf3d(1, 0, 0, 0, 0, -1, 0, -1, 0)},
  {transf3d(-1, 0, 0, 0, 0, -1, 0, -1, 0), transf3d(-1, 0, 0, 0, 0, -1, 0, -1, 0)},
  {transf3d(0, 1, 0, 0, 0, -1, -1, 0, 0), transf3d(0, 0, -1, 1, 0, 0, 0, -1, 0)},
  {transf3d(0, -1, 0, 0, 0, -1, -1, 0, 0), transf3d(0, 0, -1, -1, 0, 0, 0, -1, 0)},
  {transf3d(0, 0, 1, 0, -1, 0, -1, 0, 0), transf3d(0, 0, -1, 0, -1, 0, 1, 0, 0)},
  {transf3d(0, 0, -1, 0, -1, 0, -1, 0, 0), transf3d(0, 0, -1, 0, -1, 0, -1, 0, 0)},
  {transf3d(1, 0, 0, 0, -1, 0, 0, 0, -1), transf3d(1, 0, 0, 0, -1, 0, 0, 0, -1)},
  {transf3d(-1, 0, 0, 0, -1, 0, 0, 0, -1), transf3d(-1, 0, 0, 0, -1, 0, 0, 0, -1)},
  {transf3d(0, 1, 0, -1, 0, 0, 0, 0, -1), transf3d(0, -1, 0, 1, 0, 0, 0, 0, -1)},
  {transf3d(0, -1, 0, -1, 0, 0, 0, 0, -1), transf3d(0, -1, 0, -1, 0, 0, 0, 0, -1)},
  {transf3d(0, 0, 1, -1, 0, 0, 0, -1, 0), transf3d(0, -1, 0, 0, 0, -1, 1, 0, 0)},
  {transf3d(0, 0, -1, -1, 0, 0, 0, -1, 0), transf3d(0, -1, 0, 0, 0, -1, -1, 0, 0)},
  {transf3d(1, 0, 0, 0, 1, 0, 0, 0, -1), transf3d(1, 0, 0, 0, 1, 0, 0, 0, -1)},
  {transf3d(-1, 0, 0, 0, 1, 0, 0, 0, -1), transf3d(-1, 0, 0, 0, 1, 0, 0, 0, -1)},
  {transf3d(0, 1, 0, 1, 0, 0, 0, 0, -1), transf3d(0, 1, 0, 1, 0, 0, 0, 0, -1)},
  {transf3d(0, -1, 0, 1, 0, 0, 0, 0, -1), transf3d(0, 1, 0, -1, 0, 0, 0, 0, -1)},
  {transf3d(0, 0, 1, 1, 0, 0, 0, -1, 0), transf3d(0, 1, 0, 0, 0, -1, 1, 0, 0)},
  {transf3d(0, 0, -1, 1, 0, 0, 0, -1, 0), transf3d(0, 1, 0, 0, 0, -1, -1, 0, 0)},
  {transf3d(1, 0, 0, 0, 0, -1, 0, 1, 0), transf3d(1, 0, 0, 0, 0, 1, 0, -1, 0)},
  {transf3d(-1, 0, 0, 0, 0, -1, 0, 1, 0), transf3d(-1, 0, 0, 0, 0, 1, 0, -1, 0)},
  {transf3d(0, 1, 0, 0, 0, -1, 1, 0, 0), transf3d(0, 0, 1, 1, 0, 0, 0, -1, 0)},
  {transf3d(0, -1, 0, 0, 0, -1, 1, 0, 0), transf3d(0, 0, 1, -1, 0, 0, 0, -1, 0)},
  {transf3d(0, 0, 1, 0, -1, 0, 1, 0, 0), transf3d(0, 0, 1, 0, -1, 0, 1, 0, 0)},
  {transf3d(0, 0, -1, 0, -1, 0, 1, 0, 0), transf3d(0, 0, 1, 0, -1, 0, -1, 0, 0)}
};

// translates a generic point into the specific sector in the 1/48 space
// the specific sector is limited by following planes:
// (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 0, -1), (0, -1, 1)
// returns the transformation matrix used and also an inverse of the matrix
// that can be used to translate back
const transf3d_pair& cube_polywell_transform (vect3d& p)
{
  bool xge0 = p.x >= 0;
  bool yge0 = p.y >= 0;
  bool zge0 = p.z >= 0;
  if ( xge0 )
    {
      if ( yge0 )
        {
          if ( zge0 )
            {
              if ( p.x - p.y >= 0 )
                {
                  if ( p.x - p.z >= 0 )
                    {
                      if ( p.y - p.z >= 0 )
                        {
                          p = vect3d(p.x, p.z, p.y);
                          return transforms[0];
                        }
                      else
                        {
                          p = vect3d(p.x, p.y, p.z);
                          return transforms[6];
                        }
                    }
                  else
                    {
                      p = vect3d(p.z, p.y, p.x);
                      return transforms[4];
                    }
                }
              else
                {
                  if ( p.x - p.z >= 0 )
                    {
                      p = vect3d(p.y, p.z, p.x);
                      return transforms[2];
                    }
                  else
                    {
                      if ( p.y - p.z >= 0 )
                        {
                          p = vect3d(p.y, p.x, p.z);
                          return transforms[8];
                        }
                      else
                        {
                          p = vect3d(p.z, p.x, p.y);
                          return transforms[10];
                        }
                    }
                }
            }
          else
            {
              if ( p.x - p.y >= 0 )
                {
                  if ( p.x + p.z >= 0 )
                    {
                      if ( p.y + p.z >= 0 )
                        {
                          p = vect3d(p.x, -p.z, p.y);
                          return transforms[42];
                        }
                      else
                        {
                          p = vect3d(p.x, p.y, -p.z);
                          return transforms[36];
                        }
                    }
                  else
                    {
                      p = vect3d(-p.z, p.y, p.x);
                      return transforms[5];
                    }
                }
              else
                {
                  if ( p.x + p.z >= 0 )
                    {
                      p = vect3d(p.y, -p.z, p.x);
                      return transforms[44];
                    }
                  else
                    {
                      if ( p.y + p.z >= 0 )
                        {
                          p = vect3d(p.y, p.x, -p.z);
                          return transforms[38];
                        }
                      else
                        {
                          p = vect3d(-p.z, p.x, p.y);
                          return transforms[11];
                        }
                    }
                }
            }
        }
      else
        {
          if ( zge0 )
            {
              if ( p.x + p.y >= 0 )
                {
                  if ( p.x - p.z >= 0 )
                    {
                      if ( p.y + p.z >= 0 )
                        {
                          p = vect3d(p.x, -p.y, p.z);
                          return transforms[12];
                        }
                      else
                        {
                          p = vect3d(p.x, p.z, -p.y);
                          return transforms[18];
                        }
                    }
                  else
                    {
                      p = vect3d(p.z, -p.y, p.x);
                      return transforms[46];
                    }
                }
              else
                {
                  if ( p.x - p.z >= 0 )
                    {
                      p = vect3d(-p.y, p.z, p.x);
                      return transforms[3];
                    }
                  else
                    {
                      if ( p.y + p.z >= 0 )
                        {
                          p = vect3d(p.z, p.x, -p.y);
                          return transforms[40];
                        }
                      else
                        {
                          p = vect3d(-p.y, p.x, p.z);
                          return transforms[9];
                        }
                    }
                }
            }
          else
            {
              if ( p.x + p.y >= 0 )
                {
                  if ( p.x + p.z >= 0 )
                    {
                      if ( p.y - p.z >= 0 )
                        {
                          p = vect3d(p.x, -p.y, -p.z);
                          return transforms[30];
                        }
                      else
                        {
                          p = vect3d(p.x, -p.z, -p.y);
                          return transforms[24];
                        }
                    }
                  else
                    {
                      p = vect3d(-p.z, -p.y, p.x);
                      return transforms[47];
                    }
                }
              else
                {
                  if ( p.x + p.z >= 0 )
                    {
                      p = vect3d(-p.y, -p.z, p.x);
                      return transforms[45];
                    }
                  else
                    {
                      if ( p.y - p.z >= 0 )
                        {
                          p = vect3d(-p.z, p.x, -p.y);
                          return transforms[41];
                        }
                      else
                        {
                          p = vect3d(-p.y, p.x, -p.z);
                          return transforms[39];
                        }
                    }
                }
            }
        }
    }
  else
    {
      if ( yge0 )
        {
          if ( zge0 )
            {
              if ( p.x + p.y >= 0 )
                {
                  if ( p.x + p.z >= 0 )
                    {
                      if ( p.y - p.z >= 0 )
                        {
                          p = vect3d(p.y, -p.x, p.z);
                          return transforms[14];
                        }
                      else
                        {
                          p = vect3d(p.z, -p.x, p.y);
                          return transforms[16];
                        }
                    }
                  else
                    {
                      p = vect3d(p.y, p.z, -p.x);
                      return transforms[20];
                    }
                }
              else
                {
                  if ( p.x + p.z >= 0 )
                    {
                      p = vect3d(p.z, p.y, -p.x);
                      return transforms[22];
                    }
                  else
                    {
                      if ( p.y - p.z >= 0 )
                        {
                          p = vect3d(-p.x, p.z, p.y);
                          return transforms[1];
                        }
                      else
                        {
                          p = vect3d(-p.x, p.y, p.z);
                          return transforms[7];
                        }
                    }
                }
            }
          else
            {
              if ( p.x + p.y >= 0 )
                {
                  if ( p.x - p.z >= 0 )
                    {
                      if ( p.y + p.z >= 0 )
                        {
                          p = vect3d(p.y, -p.x, -p.z);
                          return transforms[32];
                        }
                      else
                        {
                          p = vect3d(-p.z, -p.x, p.y);
                          return transforms[17];
                        }
                    }
                  else
                    {
                      p = vect3d(p.y, -p.z, -p.x);
                      return transforms[26];
                    }
                }
              else
                {
                  if ( p.x - p.z >= 0 )
                    {
                      p = vect3d(-p.z, p.y, -p.x);
                      return transforms[23];
                    }
                  else
                    {
                      if ( p.y + p.z >= 0 )
                        {
                          p = vect3d(-p.x, -p.z, p.y);
                          return transforms[43];
                        }
                      else
                        {
                          p = vect3d(-p.x, p.y, -p.z);
                          return transforms[37];
                        }
                    }
                }
            }
        }
      else
        {
          if ( zge0 )
            {
              if ( p.x - p.y >= 0 )
                {
                  if ( p.x + p.z >= 0 )
                    {
                      if ( p.y + p.z >= 0 )
                        {
                          p = vect3d(p.z, -p.x, -p.y);
                          return transforms[34];
                        }
                      else
                        {
                          p = vect3d(-p.y, -p.x, p.z);
                          return transforms[15];
                        }
                    }
                  else
                    {
                      p = vect3d(-p.y, p.z, -p.x);
                      return transforms[21];
                    }
                }
              else
                {
                  if ( p.x + p.z >= 0 )
                    {
                      p = vect3d(p.z, -p.y, -p.x);
                      return transforms[28];
                    }
                  else
                    {
                      if ( p.y + p.z >= 0 )
                        {
                          p = vect3d(-p.x, -p.y, p.z);
                          return transforms[13];
                        }
                      else
                        {
                          p = vect3d(-p.x, p.z, -p.y);
                          return transforms[19];
                        }
                    }
                }
            }
          else
            {
              if ( p.x - p.y >= 0 )
                {
                  if ( p.x - p.z >= 0 )
                    {
                      if ( p.y - p.z >= 0 )
                        {
                          p = vect3d(-p.z, -p.x, -p.y);
                          return transforms[35];
                        }
                      else
                        {
                          p = vect3d(-p.y, -p.x, -p.z);
                          return transforms[33];
                        }
                    }
                  else
                    {
                      p = vect3d(-p.y, -p.z, -p.x);
                      return transforms[27];
                    }
                }
              else
                {
                  if ( p.x - p.z >= 0 )
                    {
                      p = vect3d(-p.z, -p.y, -p.x);
                      return transforms[29];
                    }
                  else
                    {
                      if ( p.y - p.z >= 0 )
                        {
                          p = vect3d(-p.x, -p.y, -p.z);
                          return transforms[31];
                        }
                      else
                        {
                          p = vect3d(-p.x, -p.z, -p.y);
                          return transforms[25];
                        }
                    }
                }
            }
        }
    }
}