dc.contributor.author | Demaine, Erik D. | |
dc.contributor.author | Demaine, Martin L. | |
dc.contributor.author | Eppstein, David | |
dc.contributor.author | Lubiw, Anna | |
dc.contributor.author | Uehara, Ryuhei | |
dc.contributor.author | Abel, Zachary Ryan | |
dc.date.accessioned | 2015-11-23T16:35:55Z | |
dc.date.available | 2015-11-23T16:35:55Z | |
dc.date.issued | 2014 | |
dc.identifier.isbn | 978-3-662-45802-0 | |
dc.identifier.isbn | 978-3-662-45803-7 | |
dc.identifier.issn | 0302-9743 | |
dc.identifier.issn | 1611-3349 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/100000 | |
dc.description.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. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (ODISSEI Grant EFRI-1240383) | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Expedition Grant CCF-1138967) | en_US |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/978-3-662-45803-7_23 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths | en_US |
dc.type | Article | en_US |
dc.identifier.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. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Abel, Zachary Ryan | en_US |
dc.contributor.mitauthor | Demaine, Erik D. | en_US |
dc.contributor.mitauthor | Demaine, Martin L. | en_US |
dc.relation.journal | Graph Drawing | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Abel, Zachary; Demaine, Erik D.; Demaine, Martin L.; Eppstein, David; Lubiw, Anna; Uehara, Ryuhei | en_US |
dc.identifier.orcid | https://orcid.org/0000-0003-3803-5703 | |
dc.identifier.orcid | https://orcid.org/0000-0002-4295-1117 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |