Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths
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Demaine_Flat foldings.pdf
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Author(s)
Demaine, Erik D.
Demaine, Martin L.
Eppstein, David
Lubiw, Anna
Uehara, Ryuhei
Abel, Zachary Ryan
Date Issued
2014
Journal
Graph Drawing
Publisher
Springer-Verlag
Citation
Abel, Zachary, Erik D. Demaine, Martin L. Demaine, David Eppstein, Anna Lubiw, and Ryuhei Uehara. “Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths.” Lecture Notes in Computer Science (2014): 272–283.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/978-3-662-45803-7_23
