Paper by Erik D. Demaine

Mirela Damian, Erik D. Demaine, and Robin Flatland, “Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm”, Graphs and Combinatorics, volume 30, number 1, 2014, pages 125–140.

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(n2) additional coordinate planes between every two such grid planes.

The paper is 18 pages.

The paper is available in PDF (2001k).
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Last updated May 17, 2017 by Erik Demaine.