A kinetic triangulation scheme for moving points in the plane

Haim Kaplan, Natan Rubin, Micha Sharir

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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(n2βs+2(n)log 2n) 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 at which any specific triple of points of P can become collinear, βs+2(q)=λ s+2 (q)/q, and λs+2(q) is the maximum length of Davenport-Schinzel sequences of order s+2 on q symbols. Thus, compared to the previous solution of Agarwal, Wang and Yu (2006) [4], we achieve a (slightly) improved bound on the number of discrete changes in the triangulation. In addition, we believe that our scheme is conceptually simpler, and easier to implement and analyze.

Original languageEnglish
Pages (from-to)191-205
Number of pages15
JournalComputational Geometry: Theory and Applications
Issue number4
StatePublished - 1 May 2011
Externally publishedYes


  • Kinetic data structure
  • Pseudo-triangulation
  • Treaps
  • Triangulation

ASJC Scopus subject areas

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


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