Approximation Algorithms for Finding Best Viewpoints

  • Michael E. Houle
  • Richard Webber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)

Abstract

We address the problem of finding viewpoints that preserve the relational structure of a three-dimensional graph drawing under orthographic parallel projection. Previously, algorithms for finding the best viewpoints under two natural models of viewpoint “goodness” were proposed. Unfortunately, the inherent combinatorial complexity of the problem makes finding exact solutions is impractical. In this paper, we propose two approximation algorithms for the problem, commenting on their design, and presenting results on their performance.

References

  1. 1.
    P. K. Agarwal(1991): Intersection and Decomposition Algorithms for Planar Arrangements; Cambridge University PressGoogle Scholar
  2. 2.
    P. Bose, F. Gomez, P. Ramos, G. Toussaint (1995): “Drawing Nice Projections of Objects in Space” in Proc. 3rd Int. Symp. Graph Drawing (Passau, Germany); Springer-Verlag, LNCS;:52–63Google Scholar
  3. 3.
    M. L. Braunstein (1976): Depth Perception through Motion; Academic PressGoogle Scholar
  4. 4.
    I. Bruß, A. K. Frick (1995): “Fast Interactive 3-D Graph Visualization” in Proc. 3rd Int. Symp. Graph Drawing (Passau, Germany); Springer-Verlag, LNCS; 1027:99–110CrossRefGoogle Scholar
  5. 5.
    T. Calamoneri, A. Massini (1997): “On Three-Dimensional Layout of Interconnection Networks” in Proc. 5th Int. Symp. Graph Drawing (Rome); Springer-Verlag, LNCS; 1353:64–75CrossRefGoogle Scholar
  6. 6.
    R. F. Cohen, P. D. Eades, T. Lin, F. Ruskey (1997): “Three-Dimensional Graph Drawing” in Algorithmica; 17(2):199–208MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    P. D. Eades, M. E. Houle, R. Webber (1997): “Finding the Best Viewpoints for Three-Dimensional Graph Drawings” in Proc. 5th Int. Symp. Graph Drawing (Rome); Springer-Verlag, LNCS; 1353:87–98CrossRefGoogle Scholar
  8. 8.
    H. Edelsbrunner (1987): Algorithms in Combinatorial Geometry; Springer-VerlagGoogle Scholar
  9. 9.
    J. D. Foley, A. van Dam, S. Feiner, J. Hughes (1990): Computer Graphics: Principles and Practice, 2nd ed.; Addison-WesleyGoogle Scholar
  10. 10.
    T. M. J. Fruchterman, E. M. Reingold (1991): “Graph Drawing by Force-Directed Placement” in Software-Practice and Experience; 21(11):1129–1164CrossRefGoogle Scholar
  11. 11.
    T. Kamada, S. Kawai (1988): “A Simple Method for Computing General Position in Displaying Three-Dimensional Objects” in Computer Vision, Graphics and Image Processing; 41(1):43–56CrossRefGoogle Scholar
  12. 12.
    K. Misue, P. D. Eades, W. Lai, K. Sugiyama (1995): “Layout Adjustment and the Mental Map” in J. Visual Languages and Computing; 6:183–210CrossRefGoogle Scholar
  13. 13.
    R. Motwani, P. Raghavan (1995): Randomized Algorithms; Cambridge University PressGoogle Scholar
  14. 14.
    P. H. J. M. Otten, L. P. P. P. van Ginneken (1989): The Annealing Algorithm; Kluwer AcademicGoogle Scholar
  15. 15.
    H. Plantinga, C. R. Dyer (1990): “Visibility, Occlusion, and the Aspect Graph” in Int. J. Computer Vision; 5(2):137–160CrossRefGoogle Scholar
  16. 16.
    C. Ware, G. Franck (1996): “Evaluating Stereo and Motion Cues for Visualizing Information Nets in Three Dimensions” in ACM Trans. Graphics; 15(2):121–140CrossRefGoogle Scholar
  17. 17.
    D. R. Wood (1998): “Two-Bend Three-Dimensional Orthogonal Grid Drawing of Maximum Degree Five Graphs”; in this proceedingsGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

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

Personalised recommendations