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

Boris Aronov, Alon Efrat, Vladlen Koltun, Micha Sharir

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

6 Citations (Scopus)

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)
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
Pages383-390
Number of pages8
StatePublished - 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

Fingerprint

Union
Algebraic Complexity
Combinatorial Complexity
Ball
Radius
Closed
Object

Keywords

  • Combinatorial complexity
  • Fat objects
  • Union of objects

ASJC Scopus subject areas

  • Software
  • Geometry and Topology
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety

Cite this

Aronov, B., Efrat, A., Koltun, V., & Sharir, M. (2004). On the union of κ-round objects in three and four dimensions. In Proceedings of the Annual Symposium on Computational Geometry (pp. 383-390)

On the union of κ-round objects in three and four dimensions. / Aronov, Boris; Efrat, Alon; Koltun, Vladlen; Sharir, Micha.

Proceedings of the Annual Symposium on Computational Geometry. 2004. p. 383-390.

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

Aronov, B, Efrat, A, Koltun, V & Sharir, M 2004, On the union of κ-round objects in three and four dimensions. in Proceedings of the Annual Symposium on Computational Geometry. pp. 383-390, Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04), Brooklyn, NY, United States, 6/9/04.
Aronov B, Efrat A, Koltun V, Sharir M. On the union of κ-round objects in three and four dimensions. In Proceedings of the Annual Symposium on Computational Geometry. 2004. p. 383-390
Aronov, Boris ; Efrat, Alon ; Koltun, Vladlen ; Sharir, Micha. / On the union of κ-round objects in three and four dimensions. Proceedings of the Annual Symposium on Computational Geometry. 2004. pp. 383-390
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