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Distance-Sensitive Planar Point Location

  • Boris Aronov
  • Mark de Berg
  • Marcel Roeloffzen
  • Bettina Speckmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)

Abstract

Let \(\mathcal{S}\) be a connected planar polygonal subdivision with n edges and of total area 1. We present a data structure for point location in \(\mathcal{S}\) where queries with points far away from any region boundary are answered faster. More precisely, we show that point location queries can be answered in time \(O(1+\min(\log \frac{1}{\Delta_{p}}, \log n))\), where Δ p is the distance of the query point p to the boundary of the region containing p. Our structure is based on the following result: any simple polygon P can be decomposed into a linear number of convex quadrilaterals with the following property: for any point p ∈ P, the quadrilateral containing p has area \(\Omega(\Delta_{p}^2)\).

Keywords

Medial Axis Query Point Query Time Steiner Point Simple Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Boris Aronov
    • 1
  • Mark de Berg
    • 2
  • Marcel Roeloffzen
    • 2
  • Bettina Speckmann
    • 2
  1. 1.Dept. of Computer Science and EngineeringPolytechnic Institute of NYUUSA
  2. 2.Dept. of Computer ScienceTU EindhovenThe Netherlands

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