Towards exact numerical Voronoi diagrams (invited talk)

Chee K. Yap, Vikram Sharma, Jyh Ming Lien

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Voronoi diagrams are extremely versatile Abstract: a data structure for many geometric applications. Computing this diagram "exactly" for a polyhedral set in 3-D has been a quest of computational geometers for over two decades; this quest is still unrealized. We will locate the difficulty in this quest, thanks to a recent result of Everett et al (2009). More generally, it points to the need for alternative computational models, and other notions of exactness. In this paper, we consider an alternative approach based on the well-known Subdivision Paradigm. A brief review of such algorithms for Voronoi diagrams is given. Our unique emphasis is the use of purely numerical primitives. We avoid exact (algebraic) primitives because (1) they are hard to implement correctly, and (2) they fail to take full advantage of the resolution-limited properties of subdivision.We encapsulate our numerical approach using the concept of soft primitives that conservatively converge to the exact ones in the limit. We illustrate our approach by designing the first purely numerical algorithm for the Voronoi complex of a non-degenerate polygonal set. We also discuss the critical role of filters in such algorithms. A preliminary version of our algorithm has been implemented.

Original languageEnglish (US)
Title of host publicationProceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012
Pages2-16
Number of pages15
DOIs
StatePublished - Oct 3 2012
Event2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012 - Piscataway, NJ, United States
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012

Other

Other2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012
CountryUnited States
CityPiscataway, NJ
Period6/27/126/29/12

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Keywords

  • Filters
  • Soft predicates
  • Subdivision

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Yap, C. K., Sharma, V., & Lien, J. M. (2012). Towards exact numerical Voronoi diagrams (invited talk). In Proceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012 (pp. 2-16). [6257651] (Proceedings of the 2012 9th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2012). https://doi.org/10.1109/ISVD.2012.31