[santaclaus]

This seems similar, but somewhat different than UV auto-layout in terms of the restrictions on the map. For this mapping to produce a buildable object, each flattened face must have the same area as the 3D face, and the mapping from 2D to 3D must be globally bijective. In UV-mapping, given a set of artist-specified cuts, I do not think it is always possible to obtain an area-preserving and globally bijective map. Most industrial-strength UV tools also allow artists to rescale and deform certain faces (to make it easier to paint under fine geometry, for example), which would be wouldn't make sense given the end goal of this algorithm.