Epsilon-Unfolding Orthogonal Polyhedra

Details Epsilon-Unfolding Orthogonal Polyhedra Epsilon-Unfolding Orthogonal Polyhedra

2006-02-27

arxiv.org/abs/cs/0602095v2

Computer Science

Computational Geometry

23 pages, 20 figures, 7 references. Revised version improves language and figures, updates references, and sharpens the conclu

Scientific paper

An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, may need to be as thin as epsilon = 1/2^{Omega(n)}.

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