Development of Curves on Polyhedra Via Conical Existence

Authors

Joseph OʼRourke, Smith CollegeFollow
Costin Vîlcu, Institute of Mathematics of the Romanian Academy

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.

Recommended Citation

OʼRourke, Joseph and Vîlcu, Costin, "Development of Curves on Polyhedra Via Conical Existence" (2014). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/179