Primal dividing and dual pruning: Output-sensitive construction of four-dimensional polytopes and three-dimensional Voronoi diagrams

T. M. Chan, J. Snoeyink, Chee Keng Yap

Research output: Contribution to journalArticle


In this paper, we give an algorithm for output-sensitive construction of an f-face convex hull of a set of n points in general position in E4. Our algorithm runs in O((n + f) log2 f) time and uses O(n + f) space. This is the first algorithm within a polylogarithmic factor of optimal O(n log f + f) time over the whole range of f. By a standard lifting map, we obtain output-sensitive algorithms for the Voronoi diagram or Delaunay triangulation in E3 and for the portion of a Voronoi diagram that is clipped to a convex polytope. Our approach simplifies the "ultimate convex hull algorithm" of Kirkpatrick and Seidel in E2 and also leads to improved output-sensitive results on constructing convex hulls in Ed for any even constant d > 4.

Original languageEnglish (US)
Pages (from-to)433-454
Number of pages22
JournalDiscrete and Computational Geometry
Issue number4
StatePublished - Dec 1997


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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