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Intersecting Red and Blue Line Segments in Optimal Time and Precision

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Discrete and Computational Geometry (JCDCG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

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Abstract

A common geometric problem in computer graphics and geographic information systems is to compute the arrangement of a set of n segments that can be colored red and blue so that there are no red/red or blue/blue crossings. We give a sweep algorithm that uses the minimum arithmetic precision and runs in optimal O(n log n + k) time and O(n) space to output an arrangement with k vertices, or O(n log n) time to determine k. Our initial implementation in Java can be found at http://www.cs.unc.edu/~snoeyink/demos/rbseg.

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Author information

Authors and Affiliations

  1. UNC-CH Computer Science, CB 3175 Sitterson Hall, Chapel Hill, NC, 27599-3175, USA

    Andrea Mantler & Jack Snoeyink

Authors
  1. Andrea Mantler
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  2. Jack Snoeyink
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Editor information

Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido Shimizu-shi, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2001 Springer-Verlag Berlin Heidelberg

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Mantler, A., Snoeyink, J. (2001). Intersecting Red and Blue Line Segments in Optimal Time and Precision. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_23

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  • DOI: https://doi.org/10.1007/3-540-47738-1_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

  • eBook Packages: Springer Book Archive

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