Let $[A;B]$ denote the line segment between points $A$ and $B$ in a plane.
A star-domain, or radially convex set is a set $X$ in which there is a point $x$ such that $[x;B]\subseteq X$ for every $B\in X$.
Given a point $x$ and a set $S$ of other points, I would like to use existing terminology, if it exists, to describe the following union:
$\bigcup\{[x;s]\mid s\in S\}$
The link above is the most relevant hit I found. I was expecting to possibly find something like "the star generated by $x$ and $S$" or "the radially convex hull from $x$ to $S$."
Thanks for any references.