Refinement of Three-Dimensional Orthogonal Graph Drawings

  • Benjamin Y. S. Lynn
  • Antonios Symvonis
  • David R. Wood
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1984)


In this paper we introduce a number of techniques for the refinement of three-dimensional orthogonal drawings of maximum degree six graphs. We have implemented several existing algorithms for three- dimensional orthogonal graph drawing including a number of heuristics to improve their performance. The performance of the refinements on the produced drawings is then evaluated in an extensive experimental study. We measure the aesthetic criteria of the bounding box volume, the average and maximum number of bends per edge, and the average and maximum edge length. On the same set of graphs used in Di Battista et al. [3], our main refinement algorithm improves the above aesthetic criteria by 80%, 38%, 10%, 54% and 49%, respectively.


  1. 1.
    T. Biedl and T. Chan. Cross-coloring: improving the technique by Kolmogorov and Barzdin. Technical Report CS-2000-13, University of Waterloo, Canada, 2000.Google Scholar
  2. 2.
    M. Closson, S. Gartshore, J. Johansen, and S. K. Wismath.Fully dynamic 3-dimensional orthogonal graph drawing. In Kratochvil [8], pages 49–58.Google Scholar
  3. 3.
    G. Di Battista, M. Patrignani, and F. Vargiu. A split&push approach to 3D orthogonal drawing. In Whitesides [12], pages 87–101.Google Scholar
  4. 4.
    P. Eades, C. Stirk, and S. Whitesides. The techniques of Komolgorov and Bardzin for three dimensional orthogonal graph drawings. Inform. Proc. Lett., 60(2):97–103, 1996.Google Scholar
  5. 5.
    P. Eades, A. Symvonis, and S. Whitesides. Three dimensional orthogonal graph drawing algorithms. Discrete Applied Math., 103:55–87, 2000.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    U. Föβmeier, C. Heβ, and M. Kaufmann. On improving orthogonal drawings: the 4M-algorithm. In Whitesides [12], pages 125–137.Google Scholar
  7. 7.
    A. N. Kolmogorov and Ya. M. Barzdin. On the realization of nets in 3-dimensional space. Problems in Cybernetics, 8:261–268, March 1967.Google Scholar
  8. 8.
    J. Kratochvil, editor. Proc. Graph Drawing: 7th International Symp. (GD’99), volume 1731 of Lecture Notes in Comput. Sci., Springer, 1999.Google Scholar
  9. 9.
    A. Papakostas and I. G. Tollis. Algorithms for incremental orthogonal graph drawing in three dimensions. J. Graph Algorithms Appl., 3(4):81–115, 1999.MATHMathSciNetGoogle Scholar
  10. 10.
    M. Patrignani and F. Vargiu. 3DCube: a tool for three dimensional graph drawing. In G. Di Battista, editor, Proc. Graph Drawing: 5th International Symp. (GD’97), volume 1353 of Lecture Notes in Comput. Sci., pages 284–290, Springer, 1998.Google Scholar
  11. 11.
    J. M. Six, K. G. Kakoulis, and I. G. Tollis. Refinement of orthogonal graph drawings. In Whitesides [12], pages 302–315.Google Scholar
  12. 12.
    S. Whitesides, editor. Proc. Graph Drawing: 6th International Symp. (GD’98), volume 1547 of Lecture Notes in Comput. Sci., Springer, 1998.Google Scholar
  13. 13.
    D. R. Wood. An algorithm for three-dimensional orthogonal graph drawing. In Whitesides [12], pages 332–346.Google Scholar
  14. 14.
    D. R. Wood. Three-Dimensional Orthogonal Graph Drawing. PhD thesis, School of Computer Science and Software Engineering, Monash University, Australia, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Benjamin Y. S. Lynn
    • 1
  • Antonios Symvonis
    • 1
  • David R. Wood
    • 1
  1. 1.Basser Department of Computer ScienceThe University of SydneySydneyAustralia

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