Linear precision for parametric patches Academic Article uri icon

abstract

  • 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 Pd being a birational isomorphism. Lastly, we establish the connection between linear precision 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. 2009 Springer Science+Business Media, LLC.

published proceedings

  • Advances in Computational Mathematics

author list (cited authors)

  • Garcia-Puente, L. D., & Sottile, F.

citation count

  • 12

complete list of authors

  • Garcia-Puente, Luis David||Sottile, Frank

publication date

  • August 2010