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?

  • 6
    $\begingroup$ called star-shaped $\endgroup$ – Will Jagy Jul 4 '14 at 15:48
  • 3
    $\begingroup$ en.wikipedia.org/wiki/Star_domain $\endgroup$ – mfl Jul 4 '14 at 15:49
  • $\begingroup$ @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. $\endgroup$ – MvG Jul 4 '14 at 16:43
  • $\begingroup$ @MvG I have just done it following your suggestion. $\endgroup$ – 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 $S.$

See the following link for more information:


Since you consider only the curve (or surface) limiting such a set, the usual is the boundary of the set.



for more information about the boundary of a set.

  • $\begingroup$ I thought that there might be a term more focussing on the point: The definition of the Star Domain only states that there exists some point [...]. But one can probably just describe the set as "a radially convex set for a given point", so this indeed seems to be what I have been looking for (+1, accepted - Thanks!) $\endgroup$ – Marco13 Jul 4 '14 at 18:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.