Discretization of curvature has found numerous applications particularly in the modeling of moving smooth boundaries separating two different materials and image processing. Nonetheless, there are usually several ways to address discretization of curvature, even in the case of a 1-dimenional object (a curve) depending in essence of the role of the curvature in the physical process or the problem considered. I will present two models of discretization of curvature that I was personally involved with in relation to two geometric problems where the objects considered were also convex.