{∞,∞,∞} Honeycomb in Spherical Video

{∞,∞,∞} Honeycomb in Spherical Video

This time we are applying a loxodromic Möbius transformation to animate.  The two fixed points I chose are not antipodal on the viewable sphere, and they can be placed in the same view.  Can you find them?  We are zooming away from one and towards the other, and rotating everything about both.

This is not a looping animation, so I had to render a bunch more frames to make the video a reasonable length.  The 1800 frames took about 20 hours to render.

Aside:  I've noticed that every spherical viewer available gimbal locks at the poles, which is unfortunate.  It should be easy to avoid that with quaternion rotations (like MagicCube4D does).  Anyone know of a spherical viewer without that limitation?  My favorite desktop viewer for spherical video and images so far is KolorEyes.

Relevant Links

What is a {∞,∞,∞} Honeycomb?
arxiv.org/abs/1511.02851

KolorEyes spherical viewer
www.kolor.com/kolor-eyes

MagicCube4D
http://superliminal.com/cube/cube.htm
https://www.youtube.com/watch?v=ZJr8rodlZnE&feature=share

Comments

  1. Scott VorthmannFebruary 8, 2016 at 10:13 PM

    Hate gimbal lock!  You'd think this would be part of our digital culture by now, a snippet of mouse tool code translated into a dozen programming languages.  Let's start a Github repo!

    ReplyDelete
  2. Scott VorthmannFebruary 8, 2016 at 10:18 PM

    And now that you mention it, Chrome and Android exhibit gimbal lock, too!  C'mon, Google!  Where's your math?  Mouse drag in a spherical view should be relative, an inside-out trackball.  (The meaning of down-drag doesn't change just because I'm looking at the pole of some arbitrary coordinate system.)

    ReplyDelete
  3. Minaim TiznotFebruary 9, 2016 at 2:16 AM

    Obviously out of my league.

    ReplyDelete

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