Cube Nets v2.1 - The Official Version
This is the Official [New! Improved!] Cube Unfolding video. It replaces this one I did a long time ago:
• Unfolding a Cube
As well as the various recent pilot versions of this one that preceded it (v0.0 through v2.0). The original was meant as a companion to this Tesseract Unfolding video (also from long ago):
• Unfolding a Tesseract
These two (to my surprise) became my most-watched videos, so I figured it was high time for new (improved!) versions. This new Cube Unfolding videos are part of that.
This 2.1 version is nearly the same as the 2.0 version. It fixes a minor bug that vanished the eleventh cube net from the intro graphics. There are a few other minor tweaks around the edges. It's basically the same. But better. And Official.
The dynamic color determination is based on a 3D color space based on X=red, Y=green, and Z=blue axes. All possible angles map to a unique color comprised of the orthographic projections of a unit vector aligned with the angle onto the three axes to provide an RGB color triplet.
Note that net faces take the color of their normal. And they show the complementary color on the reverse side. (anti-X=cyan, anti-Y=magenta, anti-Z=yellow)
FWIW, the Python coding was the real fun of this project. I wanted to abstract rotations of cube parts (by specifying a point, a fulcrum, and a rotation matrix). That made the unfoldings easy to specify, so I may have some fun with this toolkit. ("The Cube Net Funnies"?)
This video was made exclusively from ultra-high-speed photons and free-range electrons. The photons from this video are guaranteed to leave your viewing screen at the speed of light. The electrons are reusable and may be stored with or without refrigeration.