Finding the best viewpoints for three-dimensional graph drawings

  • Peter Eades
  • Michael E. Houle
  • Richard Webber
Drawings in the Air
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)

Abstract

In this paper we address the problem of finding the best viewpoints for three-dimensional straight-line graph drawings. We define goodness in terms of preserving the relational structure of the graph, and develop two continuous measures of goodness under orthographic parallel projection. We develop Voronoi variants to find the best viewpoints under these measures, and present results on the complexity of these diagrams.

References

  1. 1.
    P. Agarwal: Intersection and Decomposition Algorithms for Planar Arrangements, 1991; Cambridge University PressGoogle Scholar
  2. 2.
    F. Aurenhammer: “Voronoi Diagrams — A Survey of a Fundamental Geometric Data Structure” in ACM Comp. Surveys, Sep 1991; 23(3)Google Scholar
  3. 3.
    F. Aurenhammer, H. Edelsbrunner: “An Optimal Algorithm for Constructing the Weighted Voronoi Diagram in the Plane” in Patt. Recog., 1984; 17(2):251–257CrossRefGoogle Scholar
  4. 4.
    P. Bose, F. Gomez, P. Ramos, G. Toussaint: “Drawing Nice Projections of Objects in Space” in Graph Drawing (Sep 1995; Passau, Germany); pp. 52–63Google Scholar
  5. 5.
    B. Chazelle, H. Edelsbrunner: “An Optimal Algorithm for Intersecting Line Segments” in IEEE Found. Comp. Sc. (1988)Google Scholar
  6. 6.
    R. Cohen, P. Eades, T. Lin, F. Ruskey: “Three-Dimensional Graph Drawing” in Algorithmica, 1996; 17(2)Google Scholar
  7. 7.
    F. Dehne, R. Klein: “The Voronoi Diagram of Points on a Cone”; School of Computer Science, Carleton University, OttawaGoogle Scholar
  8. 8.
    G. Di Battista, P. Eades, R. Tamassia, I. Tollis: “Algorithms for Drawing Graphs: An Annotated Bibliography”, Jun 1994; http://www.cs.brown.edu/calendar/gd94/biblio.htmlGoogle Scholar
  9. 9.
    P. Eades, W. Lai, K. Misue, K. Sugiyama: “Preserving the Mental Map of a Diagram”, 1991; Research Report IIAS-RR-91-16E, Fujitsu Laboratories Ltd., JapanGoogle Scholar
  10. 10.
    P. Eades, J. Marks, S. North: “Graph-Drawing Contest Report” in Graph Drawing (Sep 1996; Berkeley, U.S.A.); pp. 129–138Google Scholar
  11. 11.
    FADIVA, VIRI: “Actual Listing of Information Visualization Systems”, 1995; http://www-cui.darmstadt.gmd.de:80/visit/Activities/Viri/visual.htmlGoogle Scholar
  12. 12.
    J. Foley, A. van Dam, S. Feiner, J. Hughes: Computer Graphics: Principles and Practice, 2nd Ed., 1990; Addison-WesleyGoogle Scholar
  13. 13.
    S. Fortune: “A Sweepline Algorithm for Voronoi Diagrams” in Algorithmica, 1987; 2(2):153–174CrossRefGoogle Scholar
  14. 14.
    T. Kamada, S. Kawai: “A Simple Method for Computing General Position in Displaying Three-Dimensional Objects” in Comp. Vision, Graphics and Image Processing, 1988; 41:43–56Google Scholar
  15. 15.
    D. Kirkpatrick: “Optimal Search in Planar Subdivisions” in SIAM J. Comp., 1983; 12(1):28–35CrossRefGoogle Scholar
  16. 16.
    H. Koike: “An Application of Three-Dimensional Visualization to Object-Oriented Programming” in Proc. Adv. Visual Interfaces (1992); pp. 180–192Google Scholar
  17. 17.
    C. Livingston: Knot Theory, 1993; Math. Assoc. AmericaGoogle Scholar
  18. 18.
    T. Munzuer, P. Burchard: “Visualizing the Structure of the World Wide Web in 3D Hyperbolic Space” in VRML (Dec 1995; San Diego, U.S.A.); pp. 33–38Google Scholar
  19. 19.
    F. Prepasata, M. Shamos: Computational Geometry: An Introduction, 1985; Springer-VerlagGoogle Scholar
  20. 20.
    B. Regan: “Information Diagrams for the DOOMed Generation” in Visual (Feb 1996; Melbourne, Australia); pp. 557–566Google Scholar
  21. 21.
    Silicon Graphics Inc.: “ivview”; UNIX Manual PageGoogle Scholar
  22. 22.
    E. Trichina, B. Thomas: “3D Interactive Animation for Visualization of Parallel Design”, 1995; Technical Report CIS-96-001, University of South AustraliaGoogle Scholar
  23. 23.
    C. Ware, G. Franck: “Evaluating Stereo and Motion Cues for Visualizing Information Nets in Three Dimensions” in ACM Trans. Graphics, Apr 1996, 15:121–140CrossRefGoogle Scholar
  24. 24.
    C. Ware, D. Hui, G. Franck: “Visualizing Object Oriented Software in Three Dimensions” in CASCON (1993)Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Peter Eades
    • 1
  • Michael E. Houle
    • 1
  • Richard Webber
    • 1
  1. 1.Department of Computer Science and Software EngineeringUniversity of NewcastleCallaghanAustralia

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