# File:Tesseract.ogv

Tesseract.ogv(Ogg Theora video file, length 36 s, 400 × 200 pixels, 662 kbps)

## Summary

 Description English: Frame synchronized comparison of the 4D orthogonal projection (left) and 4D perspective projection (right) rotated in 4D then projected and displayed in a 3D perspective view. Date Source Own work Author Jgmoxness

Detail Description:
It has 6 sets of rotations of 90 frames each. All of these rotate in steps through ${\displaystyle \theta =i2\pi /steps}$ on the horizontal (H) projection vector. The 6 sets of H,V,Z projection basis vectors are: ${\displaystyle ((\theta ,0,0),(\theta ,\theta ,0),(\theta ,{\frac {1}{2}},{\frac {1}{2}}),(\theta ,0,{\frac {3\pi }{4}}),(\theta ,{\frac {\pi }{2}},{\frac {\pi }{4}}),(\theta ,{\frac {\theta }{2}},{\frac {\theta }{4}}))}$.

4D perspective projection is accomplished by dividing x,y,z vertex dimensions by w+1 after 4D rotation (but before projection to 3D).
This is constructed from VisibLie_E8 found on TheoryOfEverything.org with the following settings:
(* This is an auto generated list from e8Flyer.nb *)
new := {
scale = 0.1;
limitToRange = False;
cylR = 0.022;
favorite = 9;
showAxes = False;
showEdges = True;
edgeVal = {1, 32};
edgeDimTrim = 4;
perspective = False;
nDcamera = 1;
range := nDcamera;
xyVwPnt = {0, 1};
zVwPnt = 1;
steps = 10;
pListName = "C4=4Cube";
p3D = " 3D";new;

Additional scripting within e8Flyer.nb to generate movie frames is also used.

## Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
 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.

## File history

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

Date/Time Thumbnail Dimensions User Comment
current 14:05, 8 April 2010 36 s, 400 × 200 (2.84 MB) Jgmoxness consistent w/anaglyph
14:26, 30 March 2010 36 s, 600 × 300 (3.39 MB) Jgmoxness improving the quality
20:57, 28 March 2010 30 s, 600 × 200 (2.03 MB) Jgmoxness again
20:27, 28 March 2010 15 s, 764 × 298 (1.67 MB) Jgmoxness cropped and slowed
20:24, 28 March 2010 15 s, 1,240 × 450 (4.21 MB) Jgmoxness cropped
18:51, 28 March 2010 15 s, 1,240 × 450 (4.21 MB) Jgmoxness got it !
19:17, 27 March 2010 8.0 s, 400 × 144 (445 KB) Jgmoxness {{Information |Description={{en|1=Comparison of the orthogonal and perspective view using 4 sets of rotations.}} |Source={{own}} |Author=Jgmoxness |Date= |Permission= |other_versions= }}
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## Global file usage

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