
Geometry : 
Subject: Re: [geometry] within(Poly, Poly)
From: Mateusz Loskot (mateusz_at_[hidden])
Date: 20130924 09:28:18
On 24 September 2013 14:13, Adam Wulkiewicz <adam.wulkiewicz_at_[hidden]> wrote:
> Mateusz Loskot wrote:
>> On 24 September 2013 13:44, Barend Gehrels <barend_at_[hidden]> wrote:
>>> On 2492013 1:22, Adam Wulkiewicz wrote:
>>>>
>>>> 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/manual2.0/ST_Within.html
>> http://postgis.net/docs/manual2.0/ST_Contains.html
>>
>> See important notes about boundary.
>>
>
> So am I bad at interpretation of the standard? E.g. here:
> OpenGISÂ® Implementation Standard for Geographic information  Simple feature
> access  Part 1: Common architecture, page 38 (even the picture)
> or here:
> http://en.wikipedia.org/wiki/DE9IM
> 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.
This sounds correct, indeed conforms to OGC SFS 1.2 (page 39):
Expressed in terms of the DE9IM:
a.Within(b) â‡” [ I(a)âˆ©I(b)â‰ âˆ… âˆ§ I(a)âˆ©E(b)=âˆ… âˆ§ B(a)âˆ©E(b)=âˆ… ] â‡”
a.Relate(b, â€œT*F**F***â€)
where I  interior, E  exterior, B  boundary.
> And e.g. here:
>
> http://postgis.net/docs/manual2.0/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?
To avoid further confusion, I'll wait for Barend's clarification (if possible).
Might be, I don't know about all assumptions for within() in Boost.Geometry,
perhaps there are differences.
Best regards,
 Mateusz Loskot, http://mateusz.loskot.net "Participation in this whole process is a form of torture" ~~ Szalony
Geometry list run by mateusz at loskot.net