Unfolding Restricted Convex Caps
Joseph O'Rourke

TL;DR
This paper presents an algorithm for unfolding a specific class of convex polyhedra called restricted convex caps, using geometric extensions to ensure the unfolded shape does not overlap.
Contribution
It introduces a novel unfolding algorithm for convex caps with quadrilateral faces over integer lattice bases, leveraging extended Cauchy's arm lemma for non-overlap guarantees.
Findings
Algorithm successfully unfolds convex caps without overlaps.
Cap faces are quadrilaterals with vertices on an integer lattice.
The method extends classical geometric lemmas for proof of non-overlap.
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.
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Taxonomy
TopicsStructural Analysis and Optimization · Advanced Materials and Mechanics · Dynamics and Control of Mechanical Systems
