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http://hdl.handle.net/10119/16094
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| 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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