Gregory's ServerAperiodic tiling is so hot right now.
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Has anyone experimented with using them for meshing? :3
aeva
13 comments
aeva
I don't know how much flexibility the construction algorithm gives to placement but it would be neat to pick subtilings that arrange relative to the isosurface in convenient ways
aeva
The penrose rhombahedra tiling pattern is described at the end of this paper if anyone is interested:
aeva
there's some nicer renderings of what I believe is the same tiling here https://fredrikskatar.blogspot.com/2012/09/?m=1 
Tom Forsyth
@aeva The whole point of the tiling is it forces your hand - you cannot place things where you want - that's why they're aperiodic! So I'm not sure why it's a good thing? Wang Tiles are the usual way to do random-looking tiling that still obeys edge constraints. That and "wavefront collapse". As usual, fancy names for fairly simple ideas. If you want spatial locality, plenty of algos use things like Hilbert curves, and that works very well.
Tom Forsyth
@aeva The main problem is that to obey the constraints can take an unbounded amount of backtracking (again, this is what makes it truly aperiodic!)
olivia mackall
@aeva i did a shader experiment with penrose tiles last month to see if they would make tiled textures look less periodic.. but it quickly became apparent that the quasiperiodic structures are very visible to the eye
olivia mackall
@aeva here's the shadertoy hack: https://www.shadertoy.com/view/ddc3RS
aeva
@oliviaselenic it looks neat on my phone although I think I need to look again on a bigger screen   |
Penrose rhombohedra might be a promising one. This pattern is constructed with an acute rhombohedra and an obtuse rhombohedra. These apparently can be divided recursively into one another, which might make it reasonably straight forward to implement.
I doubt using this as a meshing algorithm would have any significant advantages over well established methods but the results are likely to look interesting.