- Autor
- Aurenhammer, Franz
- Walzl, Gernot
- TitelStraight Skeletons and Mitered Offsets of Nonconvex Polytopes
- Datei
- DOI10.1007/s00454-016-9811-5
- Persistent Identifier
- Erschienen inDiscrete & Computational Geometry
- Band56
- Erscheinungsjahr2016
- Heft3
- Seiten743-801
- ISSN1432-0444
- Download Statistik1780
- Peer ReviewNein
- AbstractWe give a concise definition of mitered offset surfaces for nonconvex polytopes in \(\mathbb{R}^3\), 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 \(\mathbb{R}^d\), 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 \(d \ge 3\).
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