The reflex-free hull

Abstract

We propose a hull operator, the reflex-free hull, that allows us to define a 3D analogue to bays in polygons. The reflex-free hull allows a rich set of topological types, yet for polyhedral input with n edges, it remains a polyhedral set with O(n) edges. This is in contrast to other possible hull definitions that give non-planar surfaces and higher combinatorial complexity. The reflex-free hull is related to identifying cavities in computer aided design and manufacturing, but we sketch examples to indicate that computing a reflex-free hull will be a challenging problem.