Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm

Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm

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 algorit...

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Bibliographic Details
Main Authors: Damian, Mirela (Author), Demaine, Erik D. (Contributor), Flatland, Robin (Author)
Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
Format: Article
Language:English
Published: Springer-Verlag, 2014-04-07T17:58:47Z.
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Summary: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.
National Science Foundation (U.S.) (CAREER Award CCF-0347776)

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