Paper by Erik D. Demaine
- Mirela Damian, Erik D. Demaine, Robin Flatland, and Joseph O'Rourke, “Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement”, Graphs and Combinatorics, volume 33, number 5, 2017, pages 1357–1379.
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.
- This paper is also available from SpringerLink.
- The paper is available in PDF (412k).
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- Related papers:
- DeltaUnfolding_GC (Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm)
See also other papers by Erik Demaine.
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Last updated January 4, 2022 by