Comment by mk_stjames
3 days ago
That type of shape constraint would be called having a ruled surface with a Gaussian curvature of 0 everywhere, otherwise known as a 'Developable Surface'.
Fitting a -single- such surface to a set of points is nearly trivial; finding a way to best fit -multiple- such surfaces together to approximate a non-trivial shape (cloud of points) where they share edges in a way that could be joined like this paper model.... feels very NP-hard to me. This is a subset of the problem in the 3d-scan-to-CAD industry where you have a point cloud/mesh and you need to detect flat planes, cylinders, fillets, etc of a 3d scan and best-fit primitive surfaces to those areas and then join them into a manifold while respecting a bunch of other geometric and tolerance constraints.
There is a reason why there are only a few software packages that even attempt to do this, and it is almost always human-guided in some way. It's a fascinating problem.
Human problem? It's probably already solved by one of the many recent machine learning papers, often there is source on GitHub and Transformer models on HuggingFace or some random Google Drive or Biadu drive. So one such human problem is finding how to ask aXiv Assistant what the best SOTA papers for it are and searching for if they finally released code or not (hoping researchers have a real repo not a GitHub site without code). I recall that Nvidia have some clean solutions. I wish it was a more pure principled solver though with some clean code. Probably OpenEvolve could iterate on a solution to it like the circle packing problem example but 3D. Sometimes it's funny to think that there are human problems left, which itself really is a human problem.