Computing the Voronoi diagram of a 3-D polyhedron by separate computation of its symbolic and geometric parts

Michal Etzion*, Ari Rappoport

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

32 Scopus citations


The paper presents an algorithm to construct the Voronoi diagram of a 3-D linear polyhedron. The robustness and simplicity of the algorithm are due to the separation between the computation of the symbolic and geometric parts of the diagram. The symbolic part of the diagram, the Voronoi graph, is computed by a space subdivision algorithm. The computation of the Voronoi graph utilizes only relatively simple 2-D geometric computations. Given the Voronoi graph, and a geometric approximation given by the space subdivision, the construction of the geometric part is simple and reliable. An important advantage of the algorithm is that it enables local and partial computation of the Voronoi diagram. In a previous paper we have given a detailed proof of correctness of the computation of the Voronoi graph. This paper complements the previous one by detailing the algorithm and its implementation. In addition, this paper describes the computation of the geometric part of the diagram.

Original languageAmerican English
Number of pages12
StatePublished - 1999
EventProceedings of the 1999 5th ACM Symposium on Soild Modeling and Applications - Ann Arbor, MI, USA
Duration: 9 Jun 199911 Jun 1999


ConferenceProceedings of the 1999 5th ACM Symposium on Soild Modeling and Applications
CityAnn Arbor, MI, USA

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