Talk:Simple polygon

From Wikipedia, the free encyclopedia

[edit] Are noncrossing intersections at vertices allowed simple polygons?

Let me try to represent this with text.

         A-----B
          \   /
           \ /
            C            
           / \
          /   \
         E-----D

Would ABCDEC be a "simple polygon?" None of the edges intersect (except at the vertices, where they have to intersect). Should there be an additional restriction:

"Each vertex connects exactly 2 edges." With this restriction, ABCDEC would not be a simple polygon, since C connects 4 edges.

EDIT:

User sumthinelse

"iter praemium est"

I would say ABCDEC self-intersects on vertex C, and therefore is not simple. It might be worth an example image of special cases like this. Tom Ruen 22:08, 5 December 2006 (UTC)

Looking further, I see the USE of the definition, for dividing space into an inside and outside doesn't have a problem with "touching" edges or vertices. I wouldn't call such polygons simple, like above, but if they are considered such, perhaps a term like degenerate polygon would better apply.

The definition of degeneracy comes out between ABCDEC versus ABCEDC. Both look identical geometrically, but the orientation reverses. A nondegenerate simple polygon is well-defined without defining the path. —The preceding unsigned comment was added by Tomruen (talk • contribs) 22:29, 5 December 2006 (UTC).

A more interesting case would be like an Annulus (mathematics) - one convex polygon inside of another, with a double-edge connecting them, with the most interior region actually outside.

A--------B
|xxxxxxxx|
|xE---Fxx|
|x|   |xx|
|x|   |xx|
|xH-I-Gxx|
|xxx|xxxx|
D---J----C

ABCJIGFEHIJD

Is this simple? Tom Ruen 22:22, 5 December 2006 (UTC)