On the union of κ-curved objects

Alon Efrata, Matthew J. Katz

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


A (not necessarily convex) object C in the plane is κ-curved for some constant 0 < κ < 1, if it has constant description complexity, and for each point p on the boundary of C, one can place a disk B ⊆ C of radius κ · diam(C) whose boundary passes through p. 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) logn), for some constant s.

Original languageEnglish
Pages (from-to)241-254
Number of pages14
JournalComputational Geometry: Theory and Applications
Issue number4
StatePublished - 27 Dec 1999


  • Combinatorial complexity
  • Davenport-Schinzel sequences
  • Fat objects
  • Union of objects

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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

Cite this