On the union of κ-round objects in three and four dimensions

Boris Aronov, Alon Efrat, Vladlen Koltun, Micha Sharir

Research output: Contribution to conferencePaper

6 Scopus citations

Abstract

A compact body c in ℝd is κ-round if for every point p ∈ ∂c there exists a closed ball that contains p, is contained in c, and has radius κ diam c. We show that, for any fixed κ > 0, the combinatorial complexity of the union of n κ-round, not necessarily convex objects in ℝ3 (resp., in ℝ4) of constant description complexity is O(n2+ε) (resp., O(n 3+ε)) for any ε > 0, where the constant of proportionality depends on ε, κ, and the algebraic complexity of the objects. The bound is almost tight.

Original languageEnglish (US)
Pages383-390
Number of pages8
StatePublished - Sep 29 2004
EventProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States
Duration: Jun 9 2004Jun 11 2004

Other

OtherProceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
CountryUnited States
CityBrooklyn, NY
Period6/9/046/11/04

Keywords

  • Combinatorial complexity
  • Fat objects
  • Union of objects

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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    Aronov, B., Efrat, A., Koltun, V., & Sharir, M. (2004). On the union of κ-round objects in three and four dimensions. 383-390. Paper presented at Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04), Brooklyn, NY, United States.