cubecore

A library of core functions for working with 3x3x3 Rubik's cubes
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TRANSFORMATIONS.txt (1059B)


      1 Transformations can be either simple rotations or a rotation composed
      2 with a mirroring.
      3 
      4 Simple rotations are denoted by two letters corresponding to the faces
      5 to be moved to the U and F positions, respectively. For example FD is
      6 the rotation that brings the F face on top and the D face on front.
      7 
      8 A composed rotation + mirror is obtained by applying the corresponding
      9 rotation to the solved cube mirrored along the M plane.
     10 
     11 For example, to apply the transformation RBm (mirrored RB) to a cube C:
     12 	1a. Apply a mirror along the M plane to the solved cube
     13 	1b. Rotate the mirrored cube with z' y2
     14 	3.  Apply the cube C to the transformed solved cube
     15 	4.  Apply the transformations of step 1a and 1b in reverse
     16 
     17 The orientation of pieces after a rotation ignores the new position
     18 of centers.  A rotated cube can technically be inconsistent, because
     19 the parity of the edge permutation has to be adjusted considering the
     20 parity of the centers, which we ignore.
     21 
     22 The utility script mirror.sh transforms a solved, rotated cube to its
     23 mirrored and rotated version.