Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
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 exist...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Japan
2018
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| Online Access: | http://hdl.handle.net/1721.1/116250 https://orcid.org/0000-0003-3803-5703 |
| Summary: | 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. Keywords: Grid unfolding, Linear refinement, Orthogonal polyhedron, Genus 2 |
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