Proximate planar point location

  • Authors:
  • John Iacono;Stefan Langerman

  • Affiliations:
  • Polytechnic University, Brooklyn NY;Université Libre de Bruxelles, Bruxelles, Belgium

  • Venue:
  • Proceedings of the nineteenth annual symposium on Computational geometry
  • Year:
  • 2003

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Abstract

A new data structure is presented for planar point location that executes a point location query quickly if it is spatially near the previous query. Given a triangulation T of size n and a sequence of point location queries A=q1, qm, the structure presented executes qi in time O(log d(qi-1,qi)). The distance function, d, that is used is a two dimensional generalization of rank distance that counts the number of triangles in a region from qi-1 to qi. The data structure uses O(n log log n) space.