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.



Generalization of notion of convexity
I can not comment posts because of too small reputation :-) It will change I hope.


In connection with usul's comment:


Also strongly convex sets are considered. Roughly speaking, one could require that together with two points the whole lens is contained in a set. For a definition see for instance here: <http://arxiv.org/pdf/1207.4347.pdf>


