Campus Event Calendar

Event Entry

What and Who

Polyhedral topology and geometry rediscovered

John Hughes
Brown University
AG4 Group Meeting
AG 4, AG 5  
AG Audience

Date, Time and Location

Tuesday, 15 June 2004
45 Minutes
46.1 - MPII


Polyhedral topology and polyhedral differential geometry have gained a

sudden popularity in computer graphics in the last decade, as
decimation and simplification methods have become popular, and as
progress in mesh smoothing and geometry processing has
developed. Unfortunately, the earlier work on these subjects by
mathematicians has remained largely undiscovered by graphics
researchers. In this talk, I'll present some of that earlier work,
discuss the difference between the polyhedral and smooth categories in
both geometry and topology, show some proofs of the polyhedral
analogues of classical results like Jacobi's theorem and the
Fary-Milnor theorem (that every knot has total curvature greater than
4 pi), and indicate how a probabilistic approach to some aspects of
polyhedral geometry and topology can be fruitful.


Volker Blanz
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Volker Blanz, 06/11/2004 16:05 -- Created document.