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Subject: Re: [geometry] within(Poly, Poly)
From: Mateusz Loskot (mateusz_at_[hidden])
Date: 2013-09-24 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 24-9-2013 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
>> 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:
> 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 DE-9IM:
    a.Within(b) ⇔ [ I(a)∩I(b)≠∅ ∧ I(a)∩E(b)=∅ ∧ B(a)∩E(b)=∅ ] ⇔
a.Relate(b, “T*F**F***”)

where I - interior, E - exterior, B - boundary.

> And e.g. here:
> 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,
"Participation in this whole process is a form of torture" ~~ Szalony

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