Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three

Timothy M.Y. Chan, Jack Snoeyink, Chee Keng Yap

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

Abstract

In this paper, we give an algorithm for output-sensitn construction of an f-face polytope that is defined by halfspaces in E4. Our algorithm runs in O((n + /)log2 ) time and uses 0(n + f) space. This is the first algorithi within a polylogarithmic factor of optimal 0(n logf/ + f) time over the whole range of f. By a standard liftir map, we obtain output-sensitive algorithms for the Voroni diagram or Delaunay triangulation in E3 and for the portic of a Voronoi diagram that is clipped to a convex polytop Our approach also simplifies the "ultimate convex hn algorithm" of Kirkpatrick and Seidel in E2.

Original languageEnglish (US)
Title of host publicationProceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995
PublisherAssociation for Computing Machinery
Pages282-291
Number of pages10
ISBN (Electronic)0898713498
StatePublished - Jan 22 1995
Event6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 - San Francisco, United States
Duration: Jan 22 1995Jan 24 1995

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995
CountryUnited States
CitySan Francisco
Period1/22/951/24/95

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ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Chan, T. M. Y., Snoeyink, J., & Yap, C. K. (1995). Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three. In Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 (pp. 282-291). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery.