Straight skeletons and mitered offsets of nonconvex polytopes

F. Aurenhammer and G. Walzl

Abstract:

We give a concise definition of mitered offset surfaces for nonconvex polytopes in 3-space, along with a proof of existence and a discussion of basic properties. These results imply the existence of 3D straight skeletons for general nonconvex polytopes. The geometric, topological, and algorithmic features of such skeletons are investigated, including a classification of their constructing events in the generic case. Our results extend to the weighted setting, to a larger class of polytope decompositions, and to general dimensions. For (weighted) straight skeletons of an $n$-facet polytope in $d$-space, an upper bound of $O(n^d)$ on their combinatorial complexity is derived. It relies on a novel layer partition for straight skeletons, and improves the trivial bound by an order of magnitude for $d
\geq 3$.



Reference: F. Aurenhammer and G. Walzl. Straight skeletons and mitered offsets of nonconvex polytopes. Discrete & Computational Geometry, 56:743-801, 2016.