On-Line Zone Construction in Arrangements of Lines in the Plane

  • Yuval Aharoni
  • Dan Halperin
  • Iddo Hanniel
  • Sariel Har-Peled
  • Chaim Linhart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1668)


Given a finite set L of lines in the plane we wish to compute the zone of an additional curve γ in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by γ, where γ is not given in advance but rather provided online portion by portion. This problem is motivated by the computation of the area bisectors of a polygonal set in the plane. We present four algorithms which solve this problem efficiently and exactly (giving precise results even on degenerate input). We implemented the four algorithms. We present implementation details, comparison of performance, and a discussion of the advantages and shortcomings of each of the proposed algorithms.


Convex Hull Binary Search Tree Input Line Recursion Tree Single Face 
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 1999

Authors and Affiliations

  • Yuval Aharoni
    • 1
  • Dan Halperin
    • 1
  • Iddo Hanniel
    • 1
  • Sariel Har-Peled
    • 1
  • Chaim Linhart
    • 1
  1. 1.Department of Computer ScienceTel-Aviv UniversityTel-AvivIsrael

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