File:Walsh permutation 125 JF.png

Original file (4,000 × 3,880 pixels, file size: 777 KB, MIME type: image/png)

Details

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.)

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


125
+1±0+1
±0+1±0
±0±0+1
+x
+y
+z
  
&0 −1−1−1&0 −2−1−1
&1 +1−1−1&1 ±0−1−1
&2 −1+1−1&2 −2+1−1
&3 +1+1−1&3 ±0+1−1
&4 −1−1+1&4 ±0−1+1
&5 +1−1+1&5 +2−1+1
&6 −1+1+1&6 ±0+1+1
&7 +1+1+1&7 +2+1+1
xyz
−1−1−1−2−1−1
+1−1−1±0
−1+1−1−2+1−1
+1+1−1±0
−1−1+1±0−1+1
+1−1+1+2
−1+1+1±0+1+1
+1+1+1+2
xyz
−1−1−1−2−1−1
−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+1+1
xyz
−1−1−1−2−1−1
+1−1−1±0−1−1
−1−1+1+1
+1−1+1+2−1+1
−1+1−1−2+1−1
+1+1−1±0+1−1
−1+1+1+1
+1+1+1+2+1+1
−x
−y
−z

Summary

Description
neutral position

This image shows the linear transformation of an example object with a binary transformation matrix.
The inverse transformation is 125 as inverse.


 
This image was created with POV-Ray.

Related images of Walsh permutation 125
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".

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You may select the license of your choice.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current00:21, 28 December 2021Thumbnail for version as of 00:21, 28 December 20214,000 × 3,880 (777 KB)Watchduckuploaded with Pywikibot

The following page uses this file:

Global file usage

The following other wikis use this file:

Metadata