Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm
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Demaine_Unfolding orthogonal.pdf
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1.95 MB
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Author(s)
Damian, Mirela
Demaine, Erik D.
Flatland, Robin
Date Issued
November 2012
Journal
Graphs and Combinatorics
Publisher
Springer-Verlag
Citation
Damian, Mirela, Erik D. Demaine, and Robin Flatland. “Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm.” Graphs and Combinatorics 30, no. 1 (January 2014): 125–140.
Version
Author's final manuscript
Abstract
We show that every orthogonal polyhedron homeomorphic to a sphere can be unfolded without overlap while using only polynomially many (orthogonal) cuts. By contrast, the best previous such result used exponentially many cuts. More precisely, given an orthogonal polyhedron with n vertices, the algorithm cuts the polyhedron only where it is met by the grid of coordinate planes passing through the vertices, together with Θ(n [superscript 2]) additional coordinate planes between every two such grid planes.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00373-012-1257-9
