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