Linear precision for parametric patches

Frank Sottile
Texas A&M University

   Linear precision is the ability of a patch to
replicate affine functions.  While classical patches
possess linear precision, it is not clear which 
exotic patches (e.g. toric patches) have this property.
In fact, every patch has a unique reparametrization
having linear precision---but the resulting blending
functions are not necessarily rational functions.

   In this talk, I will give background and discuss
work towards a classification of toric patches for 
which this reparametrization is given by rational 
functions.   I will also explain how linear precision 
is related to maximum likelihood estimation in 
in algebraic statistics, and how to use iterative
proportional fitting from statistics to compute patches.
This is joint work with Luis Garcia, Kristian Ranestad, 
and Hans-Christian Graf von Bothmer.