# Name of shape with constant distance to a line segment [duplicate]

For a computer graphics problem I have a shape that is defined by a constant distance to a line segment:

I tried to find a name for this shape, but my Google skills have failed me. Does it have a dedicated name?

• Maybe it is a Band-Aid? google.com/… – Tomás Oct 25 '13 at 13:01
• Wow, that's a really good question. You would think a name exists for this... – rschwieb Oct 25 '13 at 13:05
• I can describe it in a few ways. It's the $R$-neighbourhood of that line. It's also a special (degenerate) case of a rounded rectangle. But a specific word for this shape? I don't know. – Arthur Oct 25 '13 at 13:17
• Assuming the main line is horizontal and $l$ long, the curve is the solution to the equation $$\max(-x-l, 0, x-l)^2 + y^2 = R^2$$ – Arthur Oct 25 '13 at 13:41
• Came up again recently on another se site: graphicdesign.stackexchange.com/q/117005/129372 – rschwieb Nov 13 '18 at 4:26

Maybe it is a ciiiiiiiiircle?

Kidding aside, I've never seen a dedicated name for it, but in metric topology one can always define the set of points at distance $R$ from a given set.

I also ran across this question in another forum which appears to be asking the same thing. It is again a lot of "I don't know a specific word for it" but the words that came up were things like "race track", "truncated circle" and "stadium." (Note while some of the posters mention elliptical shapes, the OP there clearly stated he's asking about a circle split in half reconnected with straight sides to make the shape the OP is asking about here.)

Wikipedia also suggests that in common English, the "split circle connected by lines" is often called an oval, and that this name is applied to oval tracks.

Edit: Arthur noted in the comments that if you happen to follow the link to stadium, it suggests that stadium is exactly the word you're looking for. I guess if the line gets longer, you just call it a long stadium.

In my searches for terms, I came across this article on topological skeletons which seems to be a sort of "backwards" version of this problem where you start with a shape and then find points inside that are as "central" as possible.

I got the idea then to try to find answers under the heading of shape analysis, but I also ran out of luck with search terms. It seems like a promising clue, though.

• The wiki article on oval links further to Stadium (geometry), which is actually exactly what OP's looking for. That article again suggests the name discorectangle. – Arthur Oct 25 '13 at 13:33
• @Arthur Whoa! I didn't think that link would be so relevant! Thanks very much for pointing this out! I hope you don't mind if I add a blurb about it. – rschwieb Oct 25 '13 at 13:34
• I've always referred to this as a "capsule" (after pills of the shape, and it encapsulates the segment). The general case is an "offset curve". – Mark Ping Oct 25 '13 at 16:43
• @MarkPing That's a good name for it too. – rschwieb Oct 25 '13 at 16:48
• The term "capsule" that Mark mentioned is pretty commonly used in computer graphics to refer to the 3D analogue, a cylinder capped by two hemispheres. – user856 Oct 12 '15 at 14:30

Another name is obround, which can be a noun or adjective.

ob-

(non-productive) Against; facing; a combining prefix found in verbs of Latin origin.

• That's horrible! I didn't think it possible for a word to be so ugly ;-/ – TonyK Oct 12 '15 at 14:40
• @TonyK Well, there's always "discorectangle"... – endolith Oct 12 '15 at 16:41
• Stop it! Just...stop it! – TonyK Oct 12 '15 at 18:17
• A "discorectangle" is a quadrilateral accompanied by '70s music. – user856 Oct 14 '15 at 15:46