Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
| Autor: | Damian, Mirela, Demaine, Erik, Flatland, Robin, O'Rourke, Joseph |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that every orthogonal polyhedron of genus at most 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. Comment: 22 pages, 10 figures |
| Databáze: | arXiv |
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