Comment by mk_stjames

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.