How do you chop up a tetrahedron into nicely-shaped little cubes? Here's one way, obtained a la symmetric moving frames (http://www.cs.cmu.edu/~kmcrane/Projects/SymmetricMovingFrames/index.html …). How else can you do it?pic.twitter.com/Cx3WyjYTJm
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Odgovor korisnicima @keenanisalive @AntoineVacavant
This is effectively a Catmull-Clark subdivision (with some 3D version) to get the parametric domain followed by smaller-cube refinement, btw.
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Odgovor korisnicima @amirvaxman_dgp @AntoineVacavant
Right. Here's a picture of the subdivision
@amirvaxman_dgp is talking about, which can be used to trivially convert any tetrahedral mesh into a hexahedral mesh—but with poor angles near tet vertices. Any other way to split up a tet into cubes? :-)pic.twitter.com/W2aGRA691t
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Odgovor korisnicima @keenanisalive @AntoineVacavant
Not sure you can do better---what do you do with these angles? even in the 2D quad case.
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Odgovor korisnicima @amirvaxman_dgp @AntoineVacavant
Who said anything about angles? I'm just curious about ways you can dice up a tetrahedron! :-)
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If you don't care about angles, one option is like this:pic.twitter.com/t8EoyZ8QK9
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But that has T-junctions, right?
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Not topologically- that top right face is triangular in shape, but topologically a quad.
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Odgovor korisnicima @KangarooPhysics @amirvaxman_dgp i sljedećem broju korisnika:
Ah, maybe it's actually just a distorted version of the same thing Keenan originally posted!
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Ok, I think this one is topologically different. Highly distorted angles, but still all hexahedra, meeting face to face.pic.twitter.com/a7Eln2FrBc
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