# [OSM-talk] Valid geometry for closed ways

Fri Aug 20 15:02:11 BST 2010

```Iván Sánchez Ortega wrote:
> El día Friday 20 August 2010 13:00:08, Sebastian Klein dijo:
>> what are valid geometries for closed ways that represent an area?
>
> If you want polygons to behave as in "paleo" GIS, you should refer to the
> industry standars. Specifically, to
> http://www.opengeospatial.org/standards/sfa , version 1.2.1, page 26:
> c) No two Rings in the boundary cross and the Rings in the boundary of a
> Polygon may intersect at a Point but only as a tangent, e.g.
> ∀ P ∈ Polygon, ∀ c1,c2∈P.Boundary(), c1≠c2,
> ∀ p, q ∈Point, p, q ∈ c1, p ≠ q ,
> [p ∈ c2] ⇒ [∃ δ > 0 ∍ [|p-q|<δ] ⇒ [q ∉ c2] ];

I don't really understand this one. The statement is always true since
you can choose δ := |p-q|/2

Do they mean the intersection of 2 boundary rings is always a finite set?

> Pay attention to "e": The interior of a polygon is a connected point set. In
> your example, the polygon is two connected point sets.

Yes, and the LinarRings are supposed to be simple, which by definition
does not allow self tangency.

> P.S.: Don't you just love all those UTF-8 math operators?

You are a genius. :)

Are there any reference algorithms to test for validity?

I remember someone said that "Multipolygon" would be misnomer. But
according to this specification, it fits quite well, doesn't it?

Sebastian

```