Voronoi Diagrams of Lines in 3-Space under Polyhedral Convex Distance Functions

L. Paul Chew, Klara Kedem, Micha Sharir, Boaz Tagansky, Emo Welzl

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to be O(n2α(n)log n), where α(n) is a slowly growing inverse of the Ackermann function. There are arrangements of n lines where this complexity can be as large as Ω(n2α(n)).

Original languageEnglish
Pages (from-to)238-255
Number of pages18
JournalJournal of Algorithms
Volume29
Issue number2
DOIs
StatePublished - 1 Jan 1998

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Computational Theory and Mathematics

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