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.
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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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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
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