Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
Abstract: We show that every orthogonal polyhedron of genus g ≤ 2 can be unfolded without overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron edges). This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Japan
2018
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| Online Access: | http://hdl.handle.net/1721.1/113655 https://orcid.org/0000-0003-3803-5703 |
| _version_ | 1826204872312094720 |
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| author | Damian, Mirela Flatland, Robin O’Rourke, Joseph Demaine, Erik D |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Damian, Mirela Flatland, Robin O’Rourke, Joseph Demaine, Erik D |
| author_sort | Damian, Mirela |
| collection | MIT |
| description | Abstract: We show that every orthogonal polyhedron of genus g ≤ 2 can be unfolded without overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron edges). This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques. |
| first_indexed | 2024-09-23T13:02:43Z |
| format | Article |
| id | mit-1721.1/113655 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:02:43Z |
| publishDate | 2018 |
| publisher | Springer Japan |
| record_format | dspace |
| spelling | mit-1721.1/1136552022-10-01T12:45:15Z Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement Damian, Mirela Flatland, Robin O’Rourke, Joseph Demaine, Erik D Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Demaine, Erik D Abstract: We show that every orthogonal polyhedron of genus g ≤ 2 can be unfolded without overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron edges). This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques. 2018-02-14T15:37:55Z 2018-07-01T05:00:06Z 2017-09 2017-11-18T05:56:54Z Article http://purl.org/eprint/type/JournalArticle 0911-0119 1435-5914 http://hdl.handle.net/1721.1/113655 Damian, Mirela, Erik Demaine, Robin Flatland, and Joseph O’Rourke. “Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement.” Graphs and Combinatorics 33, no. 5 (September 2017): 1357–1379. https://orcid.org/0000-0003-3803-5703 en http://dx.doi.org/10.1007/s00373-017-1849-5 Graphs and Combinatorics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer Japan KK application/pdf Springer Japan Springer Japan |
| spellingShingle | Damian, Mirela Flatland, Robin O’Rourke, Joseph Demaine, Erik D Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement |
| title | Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement |
| title_full | Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement |
| title_fullStr | Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement |
| title_full_unstemmed | Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement |
| title_short | Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement |
| title_sort | unfolding genus 2 orthogonal polyhedra with linear refinement |
| url | http://hdl.handle.net/1721.1/113655 https://orcid.org/0000-0003-3803-5703 |
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