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COMPGEOM
2010
ACM

A kinetic triangulation scheme for moving points in the plane

11 years 6 months ago
A kinetic triangulation scheme for moving points in the plane
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 λs+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. Categorie...
Haim Kaplan, Natan Rubin, Micha Sharir
Added 10 Jul 2010
Updated 10 Jul 2010
Type Conference
Year 2010
Where COMPGEOM
Authors Haim Kaplan, Natan Rubin, Micha Sharir
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