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

Timothy M.Y. Chan, Jack Snoeyink, Chee 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
VolumePart F129524
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

Other

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

Fingerprint

Voronoi Diagram
Polytopes
Output
F-space
Standard Map
Delaunay triangulation
Triangulation
Polytope
Half-space
Simplify
Diagram
Face
Range of data

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

Cite this

Chan, T. M. Y., Snoeyink, J., & Yap, C. (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 (Vol. Part F129524, pp. 282-291). Association for Computing Machinery.

Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three. / Chan, Timothy M.Y.; Snoeyink, Jack; Yap, Chee.

Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995. Vol. Part F129524 Association for Computing Machinery, 1995. p. 282-291.

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

Chan, TMY, Snoeyink, J & Yap, C 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. vol. Part F129524, Association for Computing Machinery, pp. 282-291, 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995, San Francisco, United States, 1/22/95.
Chan TMY, Snoeyink J, Yap C. 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. Vol. Part F129524. Association for Computing Machinery. 1995. p. 282-291
Chan, Timothy M.Y. ; Snoeyink, Jack ; Yap, Chee. / Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three. Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995. Vol. Part F129524 Association for Computing Machinery, 1995. pp. 282-291
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