Advertisement

Discrete & Computational Geometry

, Volume 18, Issue 4, pp 433–454 | Cite as

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

Abstract.

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 E 4 . Our algorithm runs in \(O((n+f)\log^2 f)\) 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 E 3 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 E 2 and also leads to improved output-sensitive results on constructing convex hulls in E d for any even constant d > 4.

Keywords

Convex Hull Optimal Time General Position Voronoi Diagram Delaunay Triangulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 1997

Authors and Affiliations

  • T. M. Chan
    • 1
  • J. Snoeyink
    • 1
  • Chee-Keng Yap
    • 2
  1. 1.Department of Computer Science, University of British Columbia, Vancouver, BC, Canada V6T 1Z4CA
  2. 2.Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USAUS

Personalised recommendations