  We give a precise mathematical formulation for the notions of a parametric
patch and linear precision, and establish their elementary properties. We
relate linear precision to the geometry of a particular linear projection,
giving necessary (and quite restrictive) conditions for a patch to possess
linear precision. A main focus is on linear precision for Krasauskas' toric
patches, which we show is equivalent to a certain rational map on CP^d being a
birational isomorphism. Lastly, we establish the connection between linear
presision for toric surface patches and maximum likelihood degree for discrete
exponential families in algebraic statistics, and show how iterative
proportional fitting may be used to compute toric patches.
