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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/16094

Title: Efficient Enumeration of Flat-Foldable Single Vertex Crease Patterns
Authors: Ouchi, Koji
Uehara, Ryuhei
Keywords: computational origami
enumeration algorithm
flat foldability
Kawasaki Theorem
Maekawa Theorem
Issue Date: 2019-03-01
Publisher: 電子情報通信学会
Magazine name: IEICE TRANSACTIONS on Information and Systems
Volume: E102-D
Number: 3
Start page: 416
End page: 422
DOI: 10.1587/transinf.2018FCP0004
Abstract: We investigate enumeration of distinct flat-foldable crease patterns under the following assumptions: positive integer n is given; every pattern is composed of n lines incident to the center of a sheet of paper; every angle between adjacent lines is equal to 2π/n; every line is assigned one of “mountain,” “valley,” and “flat (or consequently unfolded)”; crease patterns are considered to be equivalent if they are equal up to rotation and reflection. In this natural problem, we can use two well-known theorems for flat-foldability: the Kawasaki Theorem and the Maekawa Theorem in computational origami. Unfortunately, however, they are not enough to characterize all flat-foldable crease patterns. Therefore, so far, we have to enumerate and check flat-foldability one by one using computer. In this study, we develop the first algorithm for the above stated problem by combining these results in a nontrivial way and show its analysis of efficiency.
Rights: Copyright (C)2019 IEICE. Koji Ouchi and Ryuhei Uehara, IEICE TRANSACTIONS on Information and Systems, E102-D(3), 2019, 416-422. http://www.ieice.org/jpn/trans_online/
URI: http://hdl.handle.net/10119/16094
Material Type: publisher
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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