Straight skeletons and mitered offsets of nonconvex polytopes

Franz Aurenhammer, Gernot Christian Walzl

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We give a concise definition of mitered offset surfaces for nonconvex polytopes in \mathbbmR3, 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 \mathbbmRd, an upper bound of O(nd) 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≥3.
Original languageEnglish
Pages (from-to)743-801
JournalDiscrete & computational geometry
Volume56
Issue number3
Publication statusPublished - 8 Aug 2016

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Polytopes
Skeleton
Straight
Decomposition
Polytope
Offset Surface
Combinatorial Complexity
Facet
Trivial
Partition
Upper bound
Imply
Decompose

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Straight skeletons and mitered offsets of nonconvex polytopes. / Aurenhammer, Franz; Walzl, Gernot Christian.

In: Discrete & computational geometry, Vol. 56, No. 3, 08.08.2016, p. 743-801.

Research output: Contribution to journalArticleResearchpeer-review

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