A kinetic triangulation scheme for moving points in the plane

Haim Kaplan*, Natan Rubin, Micha Sharir

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present a simple randomized scheme for triangulating a set P of n points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of P move continuously along piecewise algebraic trajectories of constant description complexity. Our triangulation scheme experiences an expected number of O(n2 βs+2(n) log2 n) discrete changes, and handles them in a manner that satisfies all the standard requirements from a kinetic data structure: compactness, efficiency, locality and responsiveness. Here s is the maximum number of times where any specific triple of points of P can become collinear, βs+2(q) = λs+2(q)/q, and λ s+2(q) is the maximum length of Davenport-Schinzel sequences of order s + 2 on n symbols. Thus, compared to the previous solution of Agarwal et al. [4], we achieve a (slightly) improved bound on the number of discrete changes in the triangulation. In addition, we believe that our scheme is simpler to implement and analyze.

Original languageEnglish
Title of host publicationProceedings of the 26th Annual Symposium on Computational Geometry, SCG'10
Pages137-146
Number of pages10
DOIs
StatePublished - 2010
Event26th Annual Symposium on Computational Geometry, SoCG 2010 - Snowbird, UT, United States
Duration: 13 Jun 201016 Jun 2010

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

Conference26th Annual Symposium on Computational Geometry, SoCG 2010
Country/TerritoryUnited States
CitySnowbird, UT
Period13/06/1016/06/10

Keywords

  • Kinetic data structures
  • Moving points
  • Triangulation

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