A.I. Bobenko, H. Pottmann, J. Wallner
Mathematische Annalen, volume 348, issue 1, pp. 1-24, (2010)
We consider a general theory of curvatures of discrete surfaces equipped
with edgewise parallel Gauss images, and where mean and Gaussian
curvatures of faces are derived from the faces’ areas and mixed areas.
Remarkably these notions are capable of unifying notable previously
defined classes of surfaces, such as discrete isothermic minimal
surfaces and surfaces of constant mean curvature. We discuss various
types of natural Gauss images, the existence of principal curvatures,
constant curvature surfaces, Christoffel duality, Koenigs nets, contact
element nets, s-isothermic nets, and interesting special cases such as
discrete Delaunay surfaces derived from elliptic billiards.