Polyhedral topology and geometry rediscovered

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.