Abstract
There are two known ways to unfold a convex polyhedron without overlap: the star unfolding and the source unfolding, both of which use shortest paths from vertices to a source point on the surface of the polyhedron. Nonoverlap of the source unfolding is straightforward; nonoverlap of the star unfolding was proved by Aronov and O'Rourke in 1992. Our first contribution is a much simpler proof of nonoverlap of the star unfolding.
Both the source and star unfolding can be generalized to use a simple geodesic curve instead of a source point. The star unfolding from a geodesic curve cuts the geodesic curve and a shortest path from each vertex to the geodesic curve. Demaine and Lubiw conjectured that the star unfolding from a geodesic curve does not overlap. We prove a special case of the conjecture. Our special case includes the previously known case of unfolding from a geodesic loop. For the general case we prove that the star unfolding from a geodesic curve can be separated into at most two nonoverlapping pieces.
BibTeX  Entry
@InProceedings{kiazyk_et_al:LIPIcs:2015:5138,
author = {Stephen Kiazyk and Anna Lubiw},
title = {{Star Unfolding from a Geodesic Curve}},
booktitle = {31st International Symposium on Computational Geometry (SoCG 2015)},
pages = {390404},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897835},
ISSN = {18688969},
year = {2015},
volume = {34},
editor = {Lars Arge and J{\'a}nos Pach},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5138},
URN = {urn:nbn:de:0030drops51380},
doi = {10.4230/LIPIcs.SOCG.2015.390},
annote = {Keywords: unfolding, convex polyhedra, geodesic curve}
}
Keywords: 

unfolding, convex polyhedra, geodesic curve 
Seminar: 

31st International Symposium on Computational Geometry (SoCG 2015) 
Issue Date: 

2015 
Date of publication: 

11.06.2015 