Orthogonal Drawings of Cycles in 3D Space

Extended Abstract
  • Giuseppe Di Battista
  • Giuseppe Liotta
  • Anna Lubiw
  • Sue Whitesides
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1984)


Let C be a directed cycle, whose edges have each been assigned a desired direction in 3D (East, West, North, South, Up, or Down) but no length. We say that C is a shape cycle. We consider the following problem. Does there exist an orthogonal drawing Γ of C in 3D such that each edge of Γ respects the direction assigned to it and such that Γ does not intersect itself? If the answer is positive, we say that C is simple. This problem arises in the context of extending orthogonal graph drawing techniques and VLSI rectilinear layout techniques from 2D to 3D. We give a combinatorial characterization of simple shape cycles that yields linear time recognition and drawing algorithms.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Giuseppe Di Battista
    • 1
  • Giuseppe Liotta
    • 2
  • Anna Lubiw
    • 3
  • Sue Whitesides
    • 4
  1. 1.Dipartimento di Informatica ed AutomazioneUniversità di Roma TreRomaItaly
  2. 2.Dipartimento di Ingegneria Elettronica e dell’InformazioneUniversità di PerugiaPerugiaItaly
  3. 3.Department of Computer ScienceUniversity of WaterlooWaterlooCanada
  4. 4.School of Computer ScienceMcGill UniversityMontrealCanada

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