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

Comments

Archived as published. Open Access article.

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