Geometry Boost List: Re: [geometry] within(Poly, Poly)

Subject: Re: [geometry] within(Poly, Poly)
From: Adam Wulkiewicz (adam.wulkiewicz_at_[hidden])
Date: 2013-09-24 09:13:04

Mateusz Loskot wrote:
> On 24 September 2013 13:44, Barend Gehrels <barend_at_[hidden]> wrote:
>> On 24-9-2013 1:22, Adam Wulkiewicz wrote:
>>> I'm playing with the implementation of missing boolean operations.
>>> Currently I'm implementing within(Poly, Poly).
>>
>> Great!
> Indeed!
>
>>> I figured out that I'll check if there is some point of the first polygon
>>> within the second one using detail::within::point_in_polygon and then check
>>> if the first polygon's exterior ring doesn't overlap the second polygon
>>> rings. I can't use detail::disjoint::disjoint_linear because this will
>>> return false for polygons which boundries overlap. And within() should
>>> return true also for those cases. I thought I'll use
>>> boost::geometry::get_turns, the same like it's used in the implementation of
>>> the touches() algorithm. Basically I need to detect if the boundries crosses
>>> or just touches itself. Is it possible to use get_turns this way?
>>
>> Yes. One detail, in case you are not aware of this: within should return
>> false even if the whole polygon is more or less inside, touching only the
>> border from the inside. So there should be no intersections at all.
> I'd also point to PostGIS documentation (OGC specification may be a
> bit tricky to grasp it all),
> where the within/contains relations is well explained and visualised
>
> http://postgis.net/docs/manual-2.0/ST_Within.html
> http://postgis.net/docs/manual-2.0/ST_Contains.html
>
> See important notes about boundary.
>

So am I bad at interpretation of the standard? E.g. here:
OpenGIS® Implementation Standard for Geographic information - Simple 
feature access - Part 1: Common architecture, page 38 (even the picture)
or here:
http://en.wikipedia.org/wiki/DE-9IM
Within is defined as an operation which return true if there is at least 
one point of the interior of the first geometry in the interior of the 
second one and the interior and boundry of the first geometry isn't in 
the exterior of the second geometry. But boundries may overlap. It just 
must have at least one point in the interior of the second geometry. 
Covered by musn't, may be 'wholly contained' in the boundry.

And e.g. here:

http://postgis.net/docs/manual-2.0/ST_Within.html

states: It is a given that if ST_Within(A,B) is true and ST_Within(B,A) 
is true, then the two geometries are considered spatially equal.

If within() returns true only if boundries don't overlap, how those both 
functions may return true at the same time?
Another thing is that this can't work for 0-sized degenerated polygons 
because there won't be any interior.

Is my reasoning wrong at some point?

Regards,
Adam