From: orourke@grendel.csc.smith.edu (Joseph O'Rourke)
Newsgroups: comp.graphics.algorithms
Subject: Re: Unwrapping 3D Polygonal Surface
Date: 9 Feb 1996 21:40:22 GMT

In article <4f66nc$8gv@sanmateo01.pop.internex.net>,
Ed Belale <Ed@Z-Axis.com> wrote:
>I'm looking for an algorithm to unwrap a 3D polygonal surface into a flat 
>surface.  The resulting area being in one piece and undistorted.  If 
>anyone knows of publications on the subject, please let me know.  Also, if 
>anyone knows anything about how FORM Z does their surface unwrapping or 
>point me to someone to contact, I'll greatly appreciate.

I know two pieces of information that might be relevant:

1. It is a long-standing unsolved problem to determine whether or
not every convex polytope (polyhedron) can be unfolded by cutting
along edges and laid flat in the plane in one piece without overlap.

2. M. Namiki and K. Fukuda developed a set of Mathematica routines
to take a given arbitrary convex polytope and unfold it.  At the
moment I cannot find a reference to this, but I've seen it in
action.