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

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Visualization and Mathematics III

Part of the book series: Mathematics and Visualization ((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.

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References

  1. Virtual Reality Applications Center. C6. Iowa State University, Ames. http://www.vrac.iastate.edu

  2. Center for Parallel Computers. The PDC cube. Royal Institute of Technology, Stockholm. http://www.pdc.kth.se/projects/vr-cube

  3. Fraunhofer IAO. HyPI-6. Fraunhofer Institute for Industrial Engineering, Stuttgart. http://vr.iao.fhg.de/6-Side-Cave/index.en.html

  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. 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.

    Article  Google Scholar 

  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. 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. 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. 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. G. Humphreys and P. Hanrahan. A distributed graphics system for large tiled displays. IEEE Visualization, 1999.

    Google Scholar 

  11. B. Schaeffer. A Software System for Inexpensive VR via Graphics Clusters. 2000. http://www.isl.uiuc.edu/ClusteredVR/paper/dgdpaper.pdf

  12. Integrated Systems Laboratory. Syzygy. University of Illinois, Urbana. http://www.isl.uiuc.edu/ClusteredVR/ClusteredVR.htm

  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. E. Molnar. The projective interpretation of the eight 3-dimensional homogogeneous geometries. Beiträge zur Algebra und Geometrie, 38 (2): 261–288, 1997.

    MathSciNet  MATH  Google Scholar 

  15. J.R. Weeks and G.K. Francis, Conway’s ZIP proof. Amer. Math. Monthly, 106 (5): 393–399, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  16. J.R. Weeks. The Shape of Space. Dekker, 1985.

    Google Scholar 

  17. Clay Mathematics Institute. The Poincaré conjecture. http://www.claymath.org/prizeproblems/poincare.htm

  18. P. Scott. The geometries of 3-manifolds. Bull. London Math. Soc., 15: 401–487, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  19. W. P. Thurston. Three-Dimensional Geometry and Topology. Princeton University Press, Princeton, New Jersey, 1997.

    MATH  Google Scholar 

  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. C. Gunn. Visualizing hyperbolic geometry. In Computer Graphics and Mathematics, pp 299–313. Eurographics, Springer Verlag, 1992.

    Google Scholar 

  22. C. Gunn. Discrete groups and visualization of three-dimensional manifolds. Computer Graphics (Prot. SIGGRAPH ‘83), 255–262, 1993.

    Google Scholar 

  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. J. Weeks. Real-time rendering in curved spaces. IEEE Computer Graphics and Applications 22 (6): 90–99, 2002.

    Article  Google Scholar 

  25. J. Weeks. Curved spaces software. http://www.northnet.org/weeks/ CurvedSpaces/

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, IL, USA

    George K. Francis & John M. Sullivan

  2. Integrated Systems Laboratory, University of Illinois, Urbana, IL, USA

    Camille M. A. Goudeseune, Henry J. Kaczmarski & Benjamin J. Schaeffer

Authors
  1. George K. Francis
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  2. Camille M. A. Goudeseune
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  3. Henry J. Kaczmarski
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  4. Benjamin J. Schaeffer
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  5. John M. Sullivan
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Editor information

Editors and Affiliations

  1. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustraße 7, 14195, Berlin, Germany

    Hans-Christian Hege

  2. Institut für Mathematik, MA 8–3, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Konrad Polthier

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© 2003 Springer-Verlag Berlin Heidelberg

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Francis, G.K., Goudeseune, C.M.A., Kaczmarski, H.J., Schaeffer, B.J., Sullivan, J.M. (2003). Alice on the Eightfold Way: Exploring Curved Spaces in an Enclosed Virtual Reality Theater. In: Hege, HC., Polthier, K. (eds) Visualization and Mathematics III. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05105-4_16

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  • DOI: https://doi.org/10.1007/978-3-662-05105-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05682-6

  • Online ISBN: 978-3-662-05105-4

  • eBook Packages: Springer Book Archive

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