A discrete parametrized surface theory in R^3
  We propose a discrete surface theory in $\mathbb R^3$ that unites the most prevalent versions of discrete special parametrizations. This theory encapsulates a large class of discrete surfaces given by a Lax representation and, in particular, the one-parameter associated families of constant curvature surfaces. The theory is not restricted to integrable geometries, but extends to a general surface theory. 
Tim Hoffmann, Andrew O. Sageman-Furnas, Max Wardetzky
math.DG