File:Walsh permutation 137 JF.png

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Details[edit]

The square matrix above is the transformation matrix used. Below it are the coordinates of the initial cube and those of the transformed cube shown in this image. In a matrix multiplication the matrix is multiplied from the left, and the coordinates are column vectors.


The tables on the right show the same coordinates, but formatted to be read as those of the orthographic projections. Those marked with a darker frame are the ones shown in the 3D image. (Also their axes are in alphabetic order, which makes them more intuitive to read.)

(−3, −2, −1) (−1, −2, −1) (−1, 0, −1) (1, 0, −1) (−1, 0, 1) (1, 0, 1) (1, 2, 1) (3, 2, 1)


137
+1+1+1
±0+1+1
±0±0+1
 +x
 +y
 +z
  
&0 −1−1−1&0 −3−2−1
&1 +1−1−1&1 −1−2−1
&2 −1+1−1&2 −1±0−1
&3 +1+1−1&3 +1±0−1
&4 −1−1+1&4 −1±0+1
&5 +1−1+1&5 +1±0+1
&6 −1+1+1&6 +1+2+1
&7 +1+1+1&7 +3+2+1
xyz
−1−1−1−3−2−1
+1−1−1−1
−1+1−1−1±0−1
+1+1−1+1
−1−1+1−1±0+1
+1−1+1+1
−1+1+1+1+2+1
+1+1+1+3
xyz
−1−1−1−3−2−1
+1−1−1−1−2−1
−1+1−1±0
+1+1−1+1±0−1
−1−1+1−1±0+1
+1−1+1+1±0+1
−1+1+1+2
+1+1+1+3+2+1
xyz
−1−1−1−3−2−1
+1−1−1−1−2−1
−1+1−1−1±0−1
−1−1+1+1
+1+1−1+1±0−1
+1−1+1+1
−1+1+1+1+2+1
+1+1+1+3+2+1
−x
−y
−z

Summary[edit]

Description
neutral position

This image shows the linear transformation of an example object with a binary transformation matrix.
The inverse transformation is 136 as inverse.   A related transformation with a non-binary matrix is 137 as inverse.

 
This image was created with POV-Ray.
Related images of Walsh permutation 137
part of Related sets of 3-bit Walsh permutations
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

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