Alice on the Eightfold Way: Exploring Curved Spaces in an Enclosed Virtual Reality Theater

  • George K. Francis
  • Camille M. A. Goudeseune
  • Henry J. Kaczmarski
  • Benjamin J. Schaeffer
  • John M. Sullivan
Part of the Mathematics and Visualization book series (MATHVISUAL)

Summary

We describe a collaboration between mathematicians interested in visualizing curved three-dimensional spaces and researchers building next-generation virtual-reality environments such as ALICE, a six-sided, rigid-walled virtual-reality chamber. This environment integrates active-stereo imaging, wireless motion-tracking and wireless-headphone sound. To reduce cost, the display is driven by a cluster of commodity computers instead of a traditional graphics supercomputer. The mathematical application tested in this environment is an implementation of Thurston’s eight-fold way; these eight three-dimensional geometries are conjectured to suffice for describing all possible three-dimensional manifolds or universes.

Keywords

cluster architecture curved spaces virtual reality 

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References

  1. 1.
    Virtual Reality Applications Center. C6. Iowa State University, Ames. http://www.vrac.iastate.edu
  2. 2.
    Center for Parallel Computers. The PDC cube. Royal Institute of Technology, Stockholm. http://www.pdc.kth.se/projects/vr-cube
  3. 3.
    Fraunhofer IAO. HyPI-6. Fraunhofer Institute for Industrial Engineering, Stuttgart. http://vr.iao.fhg.de/6-Side-Cave/index.en.html
  4. 4.
    K. Fujii, Y. Asano, N. Kubota, and H. Tanahashi. User interface device for the immersive 6-screens display COSMOS. Sixth International Conference on Virtual Systems and Multimedia, 2000. http://wv-jp.net/got/media/COSMOS/ Google Scholar
  5. 5.
    C. Cruz-Neira, D.J. Sandin, T.A. DeFanti, R.V. Kenyon, and J.C. Hart. The CAVE: Audio-Visual Experience Automatic Virtual Environment. Communications ACM, 35 (6): 65–72, 1992.CrossRefGoogle Scholar
  6. 6.
    C. Cruz-Neira, D.J. Sandin, and T.A. DeFanti. Surround-screen projection-based virtual reality: The design and implementation of the CAVE. Computer Graphics (Proc. SIGGRAPH ‘83), 1993.Google Scholar
  7. 7.
    J. Allard, L. Lecointre, V. Gouranton, E. Melin, and B. Raffin. Net Juggler. http://www.univ-orleans.fr/SCIENCES/LIFO/Members/raffin/SHPVR/ NetJuggler.php
  8. 8.
    A. Bierbaum, C. Just, P. Hartling, and C. Cruz-Neira. Flexible application design using VR Juggler. SIGGRAPH, 2000. Conference Abstracts and Applications.Google Scholar
  9. 9.
    Y. Chen, H. Chen, D. W. Clark, Z. Liu, G. Wallace, and K. Li. Software environments for cluster-based display systems. 2001. http://www.cs.princeton.edu/omnimedia/papers.html Google Scholar
  10. 10.
    G. Humphreys and P. Hanrahan. A distributed graphics system for large tiled displays. IEEE Visualization, 1999.Google Scholar
  11. 11.
    B. Schaeffer. A Software System for Inexpensive VR via Graphics Clusters. 2000. http://www.isl.uiuc.edu/ClusteredVR/paper/dgdpaper.pdf
  12. 12.
    Integrated Systems Laboratory. Syzygy. University of Illinois, Urbana. http://www.isl.uiuc.edu/ClusteredVR/ClusteredVR.htm
  13. 13.
    M. Phillips and C. Gunn. Visualizing hyperbolic space: Unusual uses of 4 x 4 matrices. In Symposium on Interactive 3D Graphics (SIGGRAPH), 25:209–214, New York, 1992.Google Scholar
  14. 14.
    E. Molnar. The projective interpretation of the eight 3-dimensional homogogeneous geometries. Beiträge zur Algebra und Geometrie, 38 (2): 261–288, 1997.MathSciNetMATHGoogle Scholar
  15. 15.
    J.R. Weeks and G.K. Francis, Conway’s ZIP proof. Amer. Math. Monthly, 106 (5): 393–399, 1999.MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    J.R. Weeks. The Shape of Space. Dekker, 1985.Google Scholar
  17. 17.
    Clay Mathematics Institute. The Poincaré conjecture. http://www.claymath.org/prizeproblems/poincare.htm
  18. 18.
    P. Scott. The geometries of 3-manifolds. Bull. London Math. Soc., 15: 401–487, 1983.MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    W. P. Thurston. Three-Dimensional Geometry and Topology. Princeton University Press, Princeton, New Jersey, 1997.MATHGoogle Scholar
  20. 20.
    E. Gausmann, R. Lehouq, J.-P. Luminete, J.-P. Uzan, and J. Weeks. Topological lensing in spherical spaces. 2001. http://www.arXiv.org/abs/gr-gc/0106033 Google Scholar
  21. 21.
    C. Gunn. Visualizing hyperbolic geometry. In Computer Graphics and Mathematics, pp 299–313. Eurographics, Springer Verlag, 1992.Google Scholar
  22. 22.
    C. Gunn. Discrete groups and visualization of three-dimensional manifolds. Computer Graphics (Prot. SIGGRAPH ‘83), 255–262, 1993.Google Scholar
  23. 23.
    G. Francis, C. Hartman, J. Mason, U. Axen, and P. McCreary. Post-Euclidean walkabout. In VROOM - the Virtual Reality Room. SIGGRAPH, Orlando, 1994.Google Scholar
  24. 24.
    J. Weeks. Real-time rendering in curved spaces. IEEE Computer Graphics and Applications 22 (6): 90–99, 2002.CrossRefGoogle Scholar
  25. 25.
    J. Weeks. Curved spaces software. http://www.northnet.org/weeks/ CurvedSpaces/

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • George K. Francis
    • 1
  • Camille M. A. Goudeseune
    • 2
  • Henry J. Kaczmarski
    • 2
  • Benjamin J. Schaeffer
    • 2
  • John M. Sullivan
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Integrated Systems LaboratoryUniversity of IllinoisUrbanaUSA

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