Isometries of hyperbolic 3-space Here is the first of a set of animated gifs showing basic isometries of hyperbolic 3-space. This one displays a loxodromic transformation. I'll post one gif a day for a bit, but the shader rendering them all is ready for your tinkering! https://www.shadertoy.com/view/MstcWr Update based on comments I should have said a little about the banana shape. It is explained some in the shader comments, which I'll copy here. Also, see the comment thread below! This shader shows basic isometries (length preserving transformations) of hyperbolic 3-space in the upper half space model. The z=0 plane is the boundary plane-at-infinity. There are four classes of transformations: parabolic, elliptic, hyperbolic, and loxodromic. These may fix 1 or 2 ideal points on the boundary plane. In general, any Mobius transformation applied to the boundary plane will extend to an isometry of hyperbolic 3-space, but all can be built by composition of the basic transformati...
is it possible for your software to be converted to js so they run in browser or any phone?
ReplyDeletei think that'd be great!
Xah Lee, not really, at least not easily. I predict it would require a complete rewrite, though the existing code would hopefully make such an effort easier. The code is here: https://github.com/roice3/MagicTile
ReplyDeleteisn't there many framework that convert/compile .net to js?
ReplyDeletei mean, i saw many of your software that's interesting, but they can't run on browser or mac or linux. I really want to blog them etc, or use them, but the .net source basically limit them for handful of programer only. eg those interested in math, and is programing experts on windows platform.
if it's in js, so it'd run on any linux, windows, mac, and android, iphone. I think that'd increase audience some 100 fold. i think considering this is worthwhile.
Anyway, just saying.
Great! Going to try this as soon as I get home!
ReplyDeleteScott Vorthmann, cool! Feel free to open GitHub issues for anything you find. I've done little more than make sure it starts up and some puzzles load correctly.
ReplyDeleteI noticed the OpenGL canvas is offset a little for instance, which doesn't surprise me (I've heard UI doesn't always transfer perfectly in Mono). But maybe there is something I can do to avoid that... I'll go open an issue now :)
Xah Lee, I hadn’t known about them, but a quick search reveals there is, e.g. https://bridge.net/
ReplyDeleteI’d be quite surprised if it worked and shocked if it was performant, but would simultaneously be happy!
Works nicely, Roice!
ReplyDelete