Topologizing boundaries in 3D space

I have a set of closed curves (not convex, not planar) in 3D.

The goal is to produce A mesh (any will do) that is manifold and contains the closed curves as boundaries/holes.

For example like this drawing:

In the case of 2 boundaries you would get something close to the general cylinder described by the 2 boundaries.

If the boundaries were all convex and part of their own convex hull then any convex hull algorithm would produce a valid mesh.

Does anyone know of an algorithm for this or something similar? I tried point cloud meshing but my point distribution is too sparse for those methods.

• Something like this? cseweb.ucsd.edu/~alchern/projects/MinimalCurrent Feb 24, 2023 at 7:17
• @Pseudonym this looks very exciting, yes I think either that or something like that, let me dive deeper into the paper. Feb 24, 2023 at 8:00
• "The new algorithm is based on differential forms on the ambient space and does not require handling meshes" Hmm.... This might be probblematic. I do need a triangle mesh out at the end of this. Feb 24, 2023 at 8:04
• Damn... the paper is really interesting, but it also seems to be operating on a discretized grid and it seems to take 27 seconds to solve for the surface. I kinda want to try implementing this regardless because it looks awesome. But I don;t really need a minimal surface, i just need any mesh that is topologically valid and contains the curves as boundaries... Feb 24, 2023 at 8:19
• It uses a discrete grid, which you could then turn into a mesh using something like marching cubes. Feb 24, 2023 at 9:56