Reporting red-blue intersections between two sets of connected line segments

  • Julien Basch
  • Leonidas J. Guibas
  • G. D. Ramkumar
Conference paper

DOI: 10.1007/3-540-61680-2_64

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)
Cite this paper as:
Basch J., Guibas L.J., Ramkumar G.D. (1996) Reporting red-blue intersections between two sets of connected line segments. In: Diaz J., Serna M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg

Abstract

We present a new line sweep algorithm, HeapSweep, for reporting bichromatic (‘purple’) intersections between a red and a blue family of line segments. If the union of the segments in each family is connected as a point set, HeapSweep reports all k purple intersections in time O((n+k)α(n) log 3n), where n is the total number of input segments and α(n) is the familiar inverse Ackermann function. To achieve these bounds, the algorithm keeps only partial information about the vertical ordering between segments of the same color, using a new data structure called a kinetic queue. In order to analyze the running time of HeapSweep, we also show that a simple polygon containing a set of n line segments can be partitioned into monotone regions by lines cutting these segments Θ(n log n) times.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Julien Basch
    • 1
  • Leonidas J. Guibas
    • 1
  • G. D. Ramkumar
    • 1
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA

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