Straight Skeletons of Three-Dimensional Polyhedra

Authors:
Gill Barequet;David Eppstein;Michael T. Goodrich;Amir Vaxman
Affiliations:
Dept. of Computer Science, Technion--Israel Institute of Technology, Haifa, Israel 32000;Computer Science Department, Univ. of California, Irvine;Computer Science Department, Univ. of California, Irvine;Dept. of Computer Science, Technion--Israel Institute of Technology, Haifa, Israel 32000
Venue:
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Year:
2008

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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(n2) features. We provide algorithms for constructing the skeleton, which run in O( min (n2logn,klogO(1)n)) time, where kis 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.