Grid Peeling is the process of taking the integer grid points inside a convex region and repeatedly removing the convex hull vertices. By contrast, the Affine Curve-Shortening Flow (ACSF) is defined as a particular deformation of a smooth curve. It has been observed in 2017 by Eppstein, Har-Peled, and Nivasch, that, as the grid is refined, Grid Peeling converges to the Affine Curve-Shortening Flow.
As part of the M.Ed. thesis of Moritz Rüber, we have investigated the grid peeling process for special parabolas, and we could observe some striking phenomena. This has lead to the precise value of the constant that relates the two processes. With Morteza Saghafian from IST Austria, we could prove the convergence of grid peeling for the class of parabolas with vertical axis.