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A Post-Euclidean Walkabout in Virtual Environments
George Francis

MacMillan 115

Abstract: A decade ago my illiMath team of students and colleagues took our CAVE guests at SIGGRAPH93 on a post-Euclidean walkabout. On our own ten year walkabout, we met with many geometrical problems in programming virtual environments to accommodate real-time interactive computer animations of mathematical subjects. Some of these problems had to be solved repeatedly as hardware and graphics libraries changed. Others solved themselves as computers became faster. But some became more intractable due to the complexity of the enterprise.

In this talk, we presents a brief look at the geometrical problems (and some of their solutions) encountered in programming the CUBE. The CUBE is one of a handful of 6-sided CAVEs in the world. Its technology and the associated system library, Syzygy, places challenging constraints on visualizing 3D hyperbolic and spherical space. Specifically, we need efficient representations in GL(4,R) of the isometry groups, and perspective projections. This is joint work with Jeff Weeks and Matt Woodruff.

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Created: 06 Sep 2003
Last modified: 10 Oct 2003 16:13:02
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