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Upward drawings to fit surfaces

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Book cover Orders, Algorithms, and Applications (ORDAL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 831))

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Abstract

Our aim is to construct ordered sets and upward drawings of them to fit smooth two-dimensional surfaces using piecewise linear two-dimensional ones.

Theorem

For any smooth two-dimensional surface S of genus g there is an ordered set P such that

  1. (i)

    P has an upward drawing, without crossing edges, on S,

  2. (ii)

    P contains the ordered set crit(S) of critical points of S,

  3. (iii)

    if S′ is any two-dimensional surface of genus g on which P has an upward drawing, without crossing edges, then crit(S) \(\subseteq\) crit(S′).

Supported in part by N.S.E.R.C.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Ottawa, K1N 6N5, Ottawa, Canada

    S. Mehdi Hashemi

  2. Department of Computer Science, University of Ottawa, K1N 6N5, Ottawa, Canada

    Ivan Rival

Authors
  1. S. Mehdi Hashemi
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  2. Ivan Rival
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Editor information

Vincent Bouchitté Michel Morvan

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© 1994 Springer-Verlag Berlin Heidelberg

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Hashemi, S.M., Rival, I. (1994). Upward drawings to fit surfaces. In: Bouchitté, V., Morvan, M. (eds) Orders, Algorithms, and Applications. ORDAL 1994. Lecture Notes in Computer Science, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019426

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  • DOI: https://doi.org/10.1007/BFb0019426

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58274-8

  • Online ISBN: 978-3-540-48597-1

  • eBook Packages: Springer Book Archive

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