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http://hdl.handle.net/10119/15360
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| Title: | Flat foldings of plane graphs with prescribed angles and edge lengths |
| Authors: | Abel, Zachary
Demaine, Erik D.
Demaine, Martin L.
Eppstein, David
Lubiw, Anna
Uehara, Ryuhei |
| Keywords: | graph folding
paper folding
graph algorithm |
| Issue Date: | 2018 |
| Publisher: | Carleton University, Computational Geometry Laboratory |
| Magazine name: | Journal of Computational Geometry |
| Volume: | 9 |
| Number: | 1 |
| Start page: | 74 |
| End page: | 93 |
| DOI: | 10.20382/jocg.v9i1a3 |
| Abstract: | When can a plane graph with prescribed edge lengths and prescribed angles (from among {0,180∘,360∘}) be folded flat to lie in an infinitesimally thick line, without crossings? This problem generalizes the classic theory of single-vertex flat origami with prescribed mountain-valley assignment, which corresponds to the case of a cycle graph. We characterize such flat-foldable plane graphs by two obviously necessary but also sufficient conditions, proving a conjecture made in 2001: the angles at each vertex should sum to 360∘, and every face of the graph must itself be flat foldable. This characterization leads to a linear-time algorithm for testing flat foldability of plane graphs with prescribed edge lengths and angles, and a polynomial-time algorithm for counting the number of distinct folded states. |
| Rights: | Copyright (C) 2018 Authors. Zachary Abel, Erik D. Demaine, Martin L. Demaine, David Eppstein, Anna Lubiw, and Ryuhei Uehara, Journal of Computational Geometry, 9(1), 2018, 74-93. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| URI: | http://hdl.handle.net/10119/15360 |
| Material Type: | publisher |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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