Document Type

Article

Publication Date

8-1-2015

Publication Title

Annals of Mathematics and Artificial Intelligence

Abstract

Robert Lang’s Universal Molecule algorithm, a landmark in modern computational origami, is the main component of his widely used Tree Maker program for origami design. It computes a crease pattern of a convex polygonal region, starting with a compatible metric tree. Although it has been informally described in several publications, neither the full power nor the inherent limitations of the method are well understood. In this paper we introduce a rigorous mathematical formalism to relate the input metric tree, the output crease pattern and the folded uniaxial origami base produced by the Universal Molecule algorithm. We characterize the family of tree-like 3D shapes that are foldable from the computed crease patterns and give a correctness proof of the algorithm.

Keywords

Computational origami, Crease pattern, Folding

Volume

74

Issue

3

First Page

371

Last Page

400

DOI

10.1007/s10472-014-9437-3

ISSN

10122443

Rights

© the authors, 2015

Comments

Peer reviewed accepted manuscript.

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