I am searching for the correct term for the following, if it exists.

A set $X\subset \mathbb{R}^2$ is called $r$-convex if for any two points $x_1, x_2\in X$ such that there exists an arc of radius $r$ connecting these two points, at least one arc lies in the set $X$.

Note 1: Obviously, there are always two arcs of radius $r$ (if one exists) connecting two points.

Note 2: When $r\rightarrow +\infty$ we have the definition of convex set.

My main interest is efficient algorithms for computation of convex hulls based on this definition of convexity.