Unfolding Restricted Convex Caps

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.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Joseph O'Rourke
• Keywords: Convex Cap, Convex Polyhedra, CORR 2007, Education, Rectangular Base