Grid peeling is the process of repeatedly removing the convex hull vertices of the grid-points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes.

翻译：网格剥皮是一个重复移除位于给定凸曲线内部的网格点凸包顶点的过程。已有猜想认为，随着网格逐渐精细化，网格剥皮将收敛于一个连续过程——仿射曲线缩短流，该流基于曲率对曲线进行变形。我们证明该猜想对一类曲线（具有竖直轴的抛物线）成立，并确定了联系这两个过程的公式中常数因子的取值。