Document Type

Article

Publication Date

2-1-2014

Publication Title

Computational Geometry: Theory and Applications

Abstract

We establish that certain classes of simple, closed, polygonal curves on the surface of a convex polyhedron develop in the plane without overlap. Our primary proof technique shows that such curves “live on a cone,” and then develops the curves by cutting the cone along a “generator” and flattening the cone in the plane. The conical existence results support a type of source unfolding of the surface of a polyhedron, described elsewhere.

Keywords

Cones, Curve development, Polyhedra, Unfolding

Volume

47

Issue

2

First Page

149

Last Page

163

DOI

10.1016/j.comgeo.2013.08.010

ISSN

09257721

Rights

© the authors

Comments

Peer reviewed accepted manuscript.

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