I do :) I've written a tool that bakes out clifford algebra functions into glsl (using sympy/sage to generate the clifford algebra). I want to use it to play

I do :) I've written a tool that bakes out clifford algebra functions into glsl (using sympy/sage to generate the clifford algebra). I want to use it to play with volumetric data... in the web browser! Obviously that's very lofty... foolish even. If it's even possible, it'd be hard. I don't have the chops at the moment, and neither does chrome! "But I think it will be quite some time before these capabilities are exposed in a web language and also with sufficiently high resource limits to do anything non-trivial." Realistically, that's probably more what I'm actually waiting for. And GVDB could be perfect, except for its super awkward licensing and platform lock. Ugh! I think there are some other realtime VDB projects out there, so I might check into those some time. In the meanwhile, when I get around to it, I'll probably end up doing low poly ("low-simplex") stuff. A more realistic goal for the browser of today (and for my skillset) is something that can intersect lower dimensional manifolds with simplices embedded in higher dimensions. Dealing with normals will be mind bending. But I believe it can be done! My project is to play with 4D (and higher) Moebius transformations of animated polygon scenes. First, the animated polygons need to be converted into 4d polytopes. Using the intersection tool described above, the 4d scene can be "scrubbed" in a time-like way by transforming the intersecting manifold. Except that now it's possible to apply conformal transformations to the 4d polytopes before scrubbing through! This is an old demo of 3d Moebius transformations applied to key-framed polygons: http://hyperspectives.wondering.xyz/moebius/hyperhorse.html http://hyperspectives.wondering.xyz/moebius/hyperhorse.html Except that now I'm wondering about what 4d Moebius transformations look like. How do they deform animation? I'm pretty sure that under a 4d moebius transformation, all four of the horse's legs could be running at different rates without ever interfering with one another. Of course they'd all be different sizes too. Also, spatial dimensions of the horse geometry would melt into the time dimension, depending on what kind of manifold was doing the time-slicing. What would it look like??! I want to see! I might actually be able to get away with using stereographic projection/rejection for time-slicing instead of intersections, but I need to think that through very, very hard. I think it'd probably result in some gnarly polygons. By the way, another thing I'm really looking into is this: https://link.springer.com/chapter/10.1007/978-3-642-54382-1_17 https://link.springer.com/chapter/10.1007/978-3-642-54382-1_... I've managed to implement these clifford-bezier surface patches in Sage, haven't gotten around to OpenGL. EDIT: By the way, in case you're curious, the idea that the horse's legs could move at different frequencies without intersecting one another is very much related to "spacetime dilation" in the theory relativity. The principle that would keep the hyper-horse from self intersecting is conformal invariance, which is closely related to Lorentz invariance.