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

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Algorithm Engineering (WAE 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1668))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Yuval Aharoni, Dan Halperin, Iddo Hanniel, Sariel Har-Peled & Chaim Linhart

Authors
  1. Yuval Aharoni
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  2. Dan Halperin
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  3. Iddo Hanniel
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  4. Sariel Har-Peled
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  5. Chaim Linhart
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Duke University, Box 90129, Durham, NC, 27708-0129, USA

    Jeffrey S. Vitter

  2. Department of Computer Science, University of London, King’s College, Strand, London, WC2R 2LS, UK

    Christos D. Zaroliagis

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© 1999 Springer-Verlag Berlin Heidelberg

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Aharoni, Y., Halperin, D., Hanniel, I., Har-Peled, S., Linhart, C. (1999). On-Line Zone Construction in Arrangements of Lines in the Plane. In: Vitter, J.S., Zaroliagis, C.D. (eds) Algorithm Engineering. WAE 1999. Lecture Notes in Computer Science, vol 1668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48318-7_13

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  • DOI: https://doi.org/10.1007/3-540-48318-7_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66427-7

  • Online ISBN: 978-3-540-48318-2

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