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Partitioning Polygons into Tree Monotone and Y -monotone Subpolygons

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2669))

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Abstract

A polygon Q is tree monotone if, for some highest or lowest point p on Q and for any point q interior to Q, there is a y-monotone curve from p to q whose interior is interior to Q. We show how to partition an n vertex polygon P in θ (n) time into tree monotone subpolygons such that any y-monotone curve interior to P intersects at most two of the subpolygons. We then use this partition to further partition P into y-monotone subpolygons such that the number of subpolygons needed to cover any given y-monotone curve interior to P is O(log n). Our algorithm runs in θ(n) time and space which is an improvement by an O(log n) factor in time and space over the best previous result.

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Author information

Authors and Affiliations

  1. University of Waterloo, Watrloo

    Ralph P. Boland

  2. Instituto de Mathemáticas, Universidad Nacional Autónoma de México, Mexico

    Jorge Urrutia

Authors
  1. Ralph P. Boland
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  2. Jorge Urrutia
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA University of Minessota Department of Computer Science and Engineering, MN, 55455, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland UK

    Chih Jeng Kenneth Tan

  5. Département d’informatique et de recherche opérationelle Montréal, Université de Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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Boland, R.P., Urrutia, J. (2003). Partitioning Polygons into Tree Monotone and Y -monotone Subpolygons. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_92

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  • DOI: https://doi.org/10.1007/3-540-44842-X_92

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40156-8

  • Online ISBN: 978-3-540-44842-6

  • eBook Packages: Springer Book Archive

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