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)


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.


cluster architecture curved spaces virtual reality 


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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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