Dear Blender Artists,
what would be the best strategy to model So called seifert surfaces with clean topology? Seifert surfaces are surfaces where the boundary is represented by a knot:
https://mathcurve.com/surfaces.gb/seifert/seifert.shtml
i am by no means a mathematician, i aim for the aesthetic purposes of such faces. The basic ones can be done manually by eyeballing, but that does not solve the issue for fast iterations or complex surfaces. Any suggestions are welcome. Thank you very much!
Hi Okidoki,
thank you for the reply, i already read this article. The approach is somewhat usefull to begin with, but the resulting topology is, well, fairly triangulated and as such hard to use for further modeling. The approch should be one that delivers decent quad topology.
Strategy. Geometry nodes can implement parametric equations as well as form a structure that fits them. The actual trefoil knot isn’t the problem, after all you are already given the math. The difficulty is creating a shape with a “good” topology. Anyway, it is an interesting problem and at the end of this I have attached my 4.3.2 blend file. I sincerely hope you don’t mind me going beyond just providing strategy.
I’m not going to walk through the math->GN stuff since that is in the blend file, but step 1 is a matter of translating from the reference you gave. The lofting part is more interesting and probably not generically applicable to all Seifert curves. My approach was to assume that I could connect the edges of the first half of the curve to the edges of the last half. It seems to work.
However: in 2D geometries (think mobius strips) the normals we think of in 3D space don’t always resolve into what is considered “good” topology. “Outside” will meet “inside” at some edge.
Hi Glen,
already impressive results, thank you very much. My Noob/Artistic approach to “fix” the normals problem would be to add a solidify modifier with set to “complex” afterwards and then add loop cuts in edit mode. Not that elegant, but mabey you can get inspiration from how what the solidify modifier does for further improvement. Thanks anyways!
This may be so… the first calls itself “approach” and needs some familiarisation into Sverchok (even if useing a “knot” with the Extra Objects addons XYZ-function) and the second is over ten years old… using some other app (which might not work today…) I didn’t thought this as a ready solution.
Also "clean topology* for a mathematical object is not as “easy” as this might look like in the first place.
I didn’t thought this as a ready solution.