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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:

ShapeName

(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?

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    $\begingroup$ called star-shaped $\endgroup$
    – Will Jagy
    Commented Jul 4, 2014 at 15:48
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    $\begingroup$ en.wikipedia.org/wiki/Star_domain $\endgroup$
    – mfl
    Commented Jul 4, 2014 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
    Commented Jul 4, 2014 at 16:43
  • $\begingroup$ @MvG I have just done it following your suggestion. $\endgroup$
    – mfl
    Commented Jul 4, 2014 at 17:02

1 Answer 1

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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:

http://en.wikipedia.org/wiki/Star_domain

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

See

http://en.wikipedia.org/wiki/Boundary_%28topology%29

for more information about the boundary of a set.

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  • $\begingroup$ 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
    Commented Jul 4, 2014 at 18:23

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