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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/13761

Title: Flat Foldings of Plane Graphs with Prescribed Angles and Edge
Authors: Abel, Zachary
Demaine, Erik D.
Demaine, Martin
Eppstein, David
Lubiw, Anna
Ryuhei Uehara
Keywords: plane graph
folding problem
single-vertex flat origami
Issue Date: 2014-09-24
Publisher: Springer
Magazine name: Lecture Notes in Computer Science
Volume: 8871
Start page: 272
End page: 283
DOI: 10.1007/978-3-662-45803-7_23
Abstract: When can a plane graph with prescribed edge lengths and prescribed angles (from among {0,180°, 360°}) be folded at to lie in an infinitesimally thick line, without crossings? This problem generalizes the classic theory of single-vertex at origami with prescribed mountain-valley assignment, which corresponds to the case of a cycle graph. We characterize such at-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 at foldable. This characterization leads to a linear-time algorithm for testing at foldability of plane graphs with prescribed edge lengths and angles, and a polynomial-time algorithm for counting the number of distinct folded states.
Rights: This is the author-created version of Springer, Zachary Abel, Erik D. Demaine, Martin Demaine, David Eppstein, Anna Lubiw and Ryuhei Uehara, Lecture Notes in Computer Science, 8871, 2014, 272-283. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/978-3-662-45803-7_23
URI: http://hdl.handle.net/10119/13761
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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