You could have replaced a bunch of faces with larger cylindrical/conical faces (aka 3D developable surfaces) to get a more realistic look. Paper can bend!

I wonder if there are algorithms for approximating arbitrary geometries with a combination of planar, cylindrical and conical faces? Sheet metal fabrication should be facing the same constraints.

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arvinpoddar 3 days ago | parent | next [-]

Hey, I'm the original author! I should have elaborated more on this constraint. First, many papercraft models do use cylindrical/conical faces - it's just something I prefer not to do stylistically. Part of the art here is the approximation, rather than aiming for perfect realism. There's also the fact that not all paper bends the same. Papers and cardboards come in various weights and textures, so they each can curve differently. Keeping only flat faces removes these variables from the assembly.

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mk_stjames 4 days ago | parent | prev | next [-]

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.

	▲	luke-stanley 3 days ago \| parent [-]
		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.

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zaphar 4 days ago | parent | prev [-]

He specifically set a constraint for now curved surfaces. Using cylindrical and conical surfaces would have violated that constraint.

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mkl 3 days ago | parent [-]

But that's an arbitrary constraint choice that didn't need to be there. It's not inherent to the medium. He has a justification for it (curves are "flimsy and introduce variances") but that is easy to get around with perpendicular reinforcing pieces inside that constrain the curve.

	▲	zaphar 3 days ago \| parent [-]
		Arbitrary constraints are essential to any artistic endeavor. It's foundational to fostering creativity. So yes, it's an arbitrary constraint. That doesn't make it any less valid.