Source Unfoldings of Convex Polyhedra via Certain Closed Curves
Computational Geometry
2012-05-07 v1
Abstract
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q "lives on a cone" to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon.
Cite
@article{arxiv.1205.0963,
title = {Source Unfoldings of Convex Polyhedra via Certain Closed Curves},
author = {Jin-ichi Itoh and Joseph O'Rourke and Costin Vilcu},
journal= {arXiv preprint arXiv:1205.0963},
year = {2012}
}
Comments
A preliminary abstract appeared EuroCG: Proc. 25th European Workshop Comput. Geom., pages 61--64, March 2009. This full version is 19 pages long, with 9 figures