3
$\begingroup$

As you may know term "polygon" might mean few different things and its meaning has to guessed from context. By some reason I have to use few of these meaning in one place.

So I converge to the following convention:

Polygon is a cyclically ordered set of points. Then I could define its sides; I can say then if the polygon is simple; for simple polygons I can define its interior. And then I need a term for the set formed by the union of the interior and all the sides of the polygon. (Maybe "body of the polygon" or "solid polygon"?)

Did you see a term for this used somewhere (I need a term different from "polygon")?

Improve this question
$\endgroup$
10
  • 1
    $\begingroup$ @JosephO'Rourke, this is bad terminology, for me polygon is not a set, say in general $\triangle ABC\not\cong \triangle BAC$ but for solid triangles (which are sets) we always have $\blacktriangle ABC\cong \blacktriangle BAC$. $\endgroup$
    – Anton Petrunin
    Commented Jul 30, 2015 at 11:41
  • 1
    $\begingroup$ @JosephO'Rourke, I am afraid that "solid" might be associated with 3D, like "solid geometry". $\endgroup$
    – Anton Petrunin
    Commented Jul 30, 2015 at 21:19
  • 2
    $\begingroup$ closed polygonal region? $\endgroup$
    – Tom Goodwillie
    Commented Aug 1, 2015 at 11:06
  • 1
    $\begingroup$ I would say "closed polygonal domain". $\endgroup$
    – Fedor Petrov
    Commented Aug 1, 2015 at 11:44
  • 2
    $\begingroup$ Another option would be to use "polygonal chain" or "polygonal curve" for what you're calling a "polygon", and "polygon" for the closed region. $\endgroup$
    – Yoav Kallus
    Commented Aug 1, 2015 at 15:03

4 Answers 4

Reset to default
4
+50
$\begingroup$

Hull? .

Improve this answer
$\endgroup$
2
  • $\begingroup$ Not bad. The only problem, I did not see it used in this context. Thank you. $\endgroup$
    – Anton Petrunin
    Commented Aug 1, 2015 at 13:11
  • $\begingroup$ Thank you again, I think this is the best answer, although it does not answer my question. $\endgroup$
    – Anton Petrunin
    Commented Aug 8, 2015 at 12:02
2
$\begingroup$

Face, or underlying space? .

Improve this answer
$\endgroup$
3
  • $\begingroup$ Face is used in the inductive definition of polyhedron, it is a polyhedron of lower dimension, so it is not exactly set. $\endgroup$
    – Anton Petrunin
    Commented Aug 1, 2015 at 23:41
  • $\begingroup$ Well, the underlying space of the face is. $\endgroup$
    – Yoav Kallus
    Commented Aug 2, 2015 at 0:28
  • $\begingroup$ That is too long... $\endgroup$
    – Anton Petrunin
    Commented Aug 2, 2015 at 8:13
2
$\begingroup$

How about "filled-in polygon" or "filled polygon". A little searching turned up such a term used in this link in some notes on computer graphics: http://www.cs.rit.edu/~icss571/filling/

Improve this answer
$\endgroup$
0
$\begingroup$

why not speak of the compact or open polygon(al region) when refering to the region defined by the edges and, speak of the boundary if the set of edges is meant?

Or one could clarify, whether a "polygon" shall be topologically equivalent to a circle or to a disk (either closed or open).

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .