Document Type
Article
Publication Date
7-2010
Publication Title
Discrete & Computational Geometry
Abstract
We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron ℘ to a simple (nonoverlapping) planar polygon: cut along one shortest path from each vertex of ℘ toQ, and cut all but one segment of Q.
Keywords
Unfolding, Star unfolding, Convex polyhedra, Quasigeodesics, Quasigeodesic loops, Shortest paths
Volume
44
Issue
1
First Page
35
Last Page
54
DOI
dx.doi.org/10.1007/s00454-009-9223-x
ISSN
1432-0444
Recommended Citation
Itoh, Jin-ichi; O'Rourke, Joseph; and Vîlcu, Costin, "Star Unfolding Convex Polyhedra via Quasigeodesic Loops" (2010). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/53
Comments
Peer reviewed accepted manuscript. Language included at the request of the publisher: The final publication is available at Springer via http://dx.doi.org/10.1007/s00454-009-9223-x.