# Name of a shape that is intersected once by each ray that starts at a given point

Is there a particular name for a shape that is intersected exactly once by each ray that starts at a given point?

To illustrate: I'm looking for a name for shapes like the left one in this image: (This is for 2D, but the same could be applied to surfaces in higher dimensions)

I thought about a word describing the shape and its relation to the point, for example, that the shape is "convex referring to a single point", but this does not seem to be appropriate. One could possibly just call it a "circle (or sphere) with varying radius"; does anyone know if there is a more adequate name for this?

• called star-shaped – Will Jagy Jul 4 '14 at 15:48
• en.wikipedia.org/wiki/Star_domain – mfl Jul 4 '14 at 15:49
• @mfl: Want to turn that into an answer? Since the question is mostly asking for a name, finding a name (or in fact four names) together with a reasonable reference is about the best kinf of answer you can get. – MvG Jul 4 '14 at 16:43
• @MvG I have just done it following your suggestion. – mfl Jul 4 '14 at 17:02

The set that you describe is the boundary of a star-shaped domain (also called star domain, star-convex set and radially convex set). The formal definition is as follows:

A set $S$ in the Euclidean space is said to be star-shaped if there exists some point $x_0\in S$ such that for any $x\in S$ the line segment $x_0x$ is contained in $S.$