
Geometry : 
Subject: Re: [geometry] within(Poly, Poly)
From: Barend Gehrels (barend_at_[hidden])
Date: 20130924 09:27:28
Hi Adam,
On 2492013 15:13, Adam Wulkiewicz wrote:
> Mateusz Loskot wrote:
>> On 24 September 2013 13:44, Barend Gehrels <barend_at_[hidden]> wrote:
>>> On 2492013 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/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?
Probably I was bad... Thanks for the wikipage, I did not know of its
existance.
> 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/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 is new for me. I always thought that within was fully inside, I did
not look it up this morning. But maybe this is only for pointinpolygon...
I see also there: (1) /a/ is within /b/, /a/ lies in the interior of /b/.
And also (contains): /(2) b/ is within /a/. Geometry /b/ lies in the
interior of /a/. Another definition: "/a/ 'contains' /b/ iff no points
of /b/ lie in the exterior of /a/, and at least one point of the
interior of /b/ lies in the interior of /a/"
contains is reversal of within.
But indeed, (2) says there may be someting on the boundary.
More here:
http://linearthinking.blogspot.nl/2007/06/subtletiesofogccoversspatial.html
>
> 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?
> Another thing is that this can't work for 0sized degenerated polygons
> because there won't be any interior.
>
> Is my reasoning wrong at some point?
>
No, you are completely right.
Thanks, Barend
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