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Straight Skeletons of Three-Dimensional Polyhedra

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Algorithms - ESA 2008 (ESA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5193))

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Abstract

We study the straight skeleton of polyhedra in 3D. We first show that the skeleton of voxel-based polyhedra may be constructed by an algorithm taking constant time per voxel. We also describe a more complex algorithm for skeletons of voxel polyhedra, which takes time proportional to the surface-area of the skeleton rather than the volume of the polyhedron. We also show that any n-vertex axis-parallel polyhedron has a straight skeleton with O(n 2) features. We provide algorithms for constructing the skeleton, which run in O( min (n 2logn,klogO(1) n)) time, where k is the output complexity. Next, we show that the straight skeleton of a general nonconvex polyhedron has an ambiguity, suggesting a consistent method to resolve it. We prove that the skeleton of a general polyhedron has a superquadratic complexity in the worst case. Finally, we report on an implementation of an algorithm for the general case.

Work on this paper by the first and fourth authors has been supported in part by a French-Israeli Research Cooperation Grant 3-3413.

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Dan Halperin Kurt Mehlhorn

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Barequet, G., Eppstein, D., Goodrich, M.T., Vaxman, A. (2008). Straight Skeletons of Three-Dimensional Polyhedra. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_13

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  • DOI: https://doi.org/10.1007/978-3-540-87744-8_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87743-1

  • Online ISBN: 978-3-540-87744-8

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