A simple construction of a digital convex n-gon with almost minimal diameter

Abstract

The paper presents a simple, almost optimal construction of a digital convex polygon with n edges, which can be included into an m × m grid of a minimal possible size m. The construction is almost optimal in the sense that the reached value for m is not more than 1 greater than the minimal possible value; such a conclusion is derived by comparison with a theoretical lower bound, which is also derived here.