On the union of κ-curved objects

Alon Efrata; Matthew J. Katz

doi:10.1016/s0925-7721(99)00036-x

On the union of κ-curved objects

Alon Efrata, Matthew J. Katz

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

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(λ_s (n) logn), for some constant s.

Original language	English
Pages (from-to)	241-254
Number of pages	14
Journal	Computational Geometry: Theory and Applications
Volume	14
Issue number	4
DOIs	https://doi.org/10.1016/s0925-7721(99)00036-x
State	Published - 27 Dec 1999

Keywords

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

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10.1016/s0925-7721(99)00036-x

Cite this

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On the union of κ-curved objects

Abstract

Keywords

ASJC Scopus subject areas

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