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Unfolding Restricted Convex Caps (0709.1647v1)
Published 11 Sep 2007 in cs.CG
Abstract: This paper details an algorithm for unfolding a class of convex polyhedra, where each polyhedron in the class consists of a convex cap over a rectangular base, with several restrictions: the cap's faces are quadrilaterals, with vertices over an underlying integer lattice, and such that the cap convexity is ``radially monotone,'' a type of smoothness constraint. Extensions of Cauchy's arm lemma are used in the proof of non-overlap.