On intersection searching problems involving curved objects

  • Prosenjit Gupta
  • Ravi Janardan
  • Michiel Smid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 824)


Efficient solutions are given for the problem of preprocessing a set of linear or curved geometric objects (e.g. lines, line segments, circles, circular arcs, d-balls, d-spheres) such that the ones that are intersected by a curved query object can be reported (or counted) quickly. The problem is considered both in the standard setting (where one is interested in all the objects intersected) and in a generalized setting (where the input objects come aggregated in disjoint groups and one is interested in the disjoint groups that are intersected). The solutions are based on geometric transformations, simplex compositions, persistence, and, for the generalized problem, on a method to progressively eliminate groups that cannot possibly be intersected.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Prosenjit Gupta
    • 1
  • Ravi Janardan
    • 1
  • Michiel Smid
    • 2
  1. 1.Department of Computer ScienceUniversity of MinnesotaMinneapolisUSA
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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