Straight Skeletons of Three-Dimensional Polyhedra

  • Gill Barequet
  • David Eppstein
  • Michael T. Goodrich
  • Amir Vaxman
Conference paper

DOI: 10.1007/978-3-540-87744-8_13

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)
Cite this paper as:
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

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 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gill Barequet
    • 1
  • David Eppstein
    • 2
  • Michael T. Goodrich
    • 2
  • Amir Vaxman
    • 1
  1. 1.Dept. of Computer ScienceTechnion—Israel Institute of TechnologyHaifaIsrael
  2. 2.Computer Science DepartmentUniv. of CaliforniaIrvine

Personalised recommendations