Mathematics for 3D modeling
March 31, 2021 9:22 AM   Subscribe

Do you know of any material that talks about mathematical invariants and methods that are useful in 3D modeling (that is, making and editing models with a modeling program)? I'll add more details about the kind of modeling and math I have in mind below.

I am teaching myself 3D modeling with Blender as a hobby, specifically the kind where model structure consists of vertices, edges and faces, forming a polygon mesh. I have learned that 3D meshes are considered to have ideal topology when they are made of quad polygons only and have clean edge flow, and it's a good idea to aim for this ideal as much as is practical. (3D modelers have adapted terminology from topology, including the word itself, in some very specific ways. My question isn't about topology in general, which I understand is quite the large field these days. I also don't need a refresher in basic 3D math used in computer graphics.)

I have found a lot of good modeling tutorials and explanations (example) that don't assume any mathematical background, and they have taught me many things while remaining vague about why some things happen the way they do. I would also like to see some material that does assume math knowledge and teaches useful methods and rules (invariants). I have in fact worked out a few rules about how local decisions affect other parts of the mesh, because of structural restrictions that a quad topology imposes. It would be helpful to have a better understanding of this aspect of modelling.
posted by primal to Computers & Internet (3 answers total) 3 users marked this as a favorite
 
Maybe take a look at the Graphics Gems books. They are an informal 'best of' papers from the early years of 3d development. I think the pdfs are free online.
posted by sammyo at 11:00 AM on March 31, 2021 [2 favorites]


Take a look at annual proceedings from SimAud - Symposium on Simulation for Architecture and Urban Design, but also other fields like acoustics.

Check out Paul Bourke's blog - covers a lot of CAD objects theory and applications. It's inspiring when I'm stuck with a tech. issue.
posted by unearthed at 11:27 AM on March 31, 2021 [1 favorite]


Best answer: I don't know where to find this kind of guide, and I agree it would be interesting to get into the math underlying mesh topology. Only place I can think to look would be SIGGRAPH papers. You might have to go back to the 80s/90s since these days mesh modeling is fairly well established and not subject to too much research, but I bet someone wrote about it at some point.
posted by Alterscape at 8:15 AM on April 1, 2021


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