Document Type
Article
Publication Date
3-1-2016
Publication Title
Mathematics in Computer Science
Abstract
The first phase of TreeMaker, a well-known method for origami design, decomposes a planar polygon (the “paper”) into regions. If some region is not convex, TreeMaker indicates it with an error message and stops. Otherwise, a second phases is invoked which computes a crease pattern called a “universal molecule”. In this paper we introduce and study geodesic universal molecules, which also work with non-convex polygons and thus extend the applicability of the TreeMaker method. We characterize the family of disk-like surfaces, crease patterns and folded states produced by our generalized algorithm. They include non-convex polygons drawn on the surface of an intrinsically flat piecewise-linear surface which have self-overlap when laid open flat, as well as surfaces with negative curvature at a boundary vertex.
Keywords
Algorithmic origami, Metric tree, Non-convex polygon, Planar subdivision
Volume
10
Issue
1
First Page
115
Last Page
141
DOI
10.1007/s11786-016-0253-5
ISSN
16618270
Rights
© Springer International Publishing 2016
Recommended Citation
Bowers, John C. and Streinu, Ileana, "Geodesic Universal Molecules" (2016). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/299
Comments
Archived as published. Open Access article.