On the union of κ-curved objects

Alon Efrat, Matthew J. Katz

Research output: Contribution to conferencePaperpeer-review

11 Scopus citations


A (not necessarily convex) object C in the plane is κ-curved for some constant κ, κ<1, if it has constant description complexity, and for each point p on the boundary of C, one can place a disk B whose boundary passes through p, its radius is κ·diam(C) and it is contained in C. We prove that the combinatorial complexity of the boundary of the union of a set C of n κ-curved objects (e.g., fat ellipses or rounded heart-shaped objects) is O(λs(n)log n), for some constant s.

Original languageEnglish
Number of pages8
StatePublished - 1 Jan 1998
Externally publishedYes
EventProceedings of the 1998 14th Annual Symposium on Computational Geometry - Minneapolis, MN, USA
Duration: 7 Jun 199810 Jun 1998


ConferenceProceedings of the 1998 14th Annual Symposium on Computational Geometry
CityMinneapolis, MN, USA

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics


Dive into the research topics of 'On the union of κ-curved objects'. Together they form a unique fingerprint.

Cite this