[postgis-users] ST_Contains - WGS84

[Martin Davis]

Regina is both right and wrong, I think.

Right, in that the spatial relationship functions are topological, and 
are not "aware" of the coordinate system of the geometry that is passed 
to them.  They will always be valid for the topological relationship of 
the inputs, but they *assume* that the inputs lie in a planar space, and 
have straight lines between their vertices.

Wrong, in that this assumption of planarity and linear edges does not 
hold for geometry which is defined in a non-planar coordinate system 
(ie. geodetic).  In this case the edges are not linear, they are arcs on 
the spheroid.  One result of this is what Markus pointed out - points 
can "jump" from one side of an edge to another.  Or more precisely, a 
point which lies on one side of a linear edge between two vertices might 
lie on the other side of the spheroidal arc between those two vertices.  
This means that the spatial predicates do not always match the 
relationship that holds on the spheroid (They do correctly provide the 
true relationship in a planar space - but for a geodetic coordinate 
system this is usually not what is expected).

There's no ideal way of correcting this.  It can be mitigated somewhat 
by densifying geodetic geometry before relating it, or by projecting to 
a local planar coordinate system.

But, I think there is a bit of good news.  I'm pretty sure that if you 
are querying in lat-long space, relationships like ST_contains end up 
being *more inclusive*.  (I.e. you may get points returned which 
wouldn't actually lie in the geometry if it was densified).  This is due 
to the fact that the spheroid "blows up like a balloon" and curves lines 
outward.  This is probably better than the alternative of being *less 
inclusive*.

This also means that there is no problem using the standard PostGIS 
spatial index on geodetic data - the index is only an approximation 
anyway, so as long as it doesn't lose geometry (which it won't by the 
argument above) it will work fine.

Of course, the other issue with handling geodetic data is dealing with 
the poles and the 180th meridian.  There's no great solution for this, 
unfortunately.  You can't query across the poles or dateline and expect 
the query to "wrap around".

Martin



Obe, Regina wrote:
> Will,
>
> I could be way off base here because I don't think too much about
> geometries except in my little world so maybe someone can correct me if
> my assumptions are way off base.
>
> Topological relations and processes like ST_Contains, ST_Intersection,
> ST_Intersects are operations that are always valid regardless of if your
> data is projected or unprojected.
>
> If a contains b in WGS 84 long lat space, a will contain b in any
> projection  you can project them to (and vice versa).  I think about
> these things as just wrapping rubber bands around stuff. No matter how
> you distort the shape of the rubber band, things inside it are always
> inside it.
>
> Now as far as indexes go - they wouldn't be as efficient in
> non-projected space because a box in unprojected has less meaning (since
> its a planar thing in spherical space).  So your operation will work but
> it will be slower since you'll get more false positives.  
>
> An extent will always contain the geometry in question regardless of
> projection (although the extent of unprojected would be different from
> if you had it in planar).  Regardless - all objects contained within an
> object should always have extents that intersect the extent of the
> object that contains them in any space.  So my thought process tells me,
> you shouldn't get any points left out, you'll just get more false
> positives from the && operation and thus slower performance.
>
> So just keep your data in SRID 4326  do your contains in that and see
> how slow it is.  May not be all that slow.
>
> Hope that helps,
> Regina
>
>
>
>
>
> -----Original Message-----
> From: postgis-users-bounces at postgis.refractions.net
> [mailto:postgis-users-bounces at postgis.refractions.net] On Behalf Of
> William Temperley
> Sent: Friday, June 27, 2008 4:49 AM
> To: postgis-users at postgis.refractions.net
> Subject: [postgis-users] ST_Contains - WGS84
>
> Hi all
>
> Is there currently an accurate way to run queries like ST_Contains on
> geodetic data?
>
> My dataset is global and I may have to perform queries on a
> continental scale, e.g. find all the points in Africa.  I don't think
> I can reproject to the UTM zone in question, given the queries will
> span several zones.  Is there a projection I can use temporarily to
> perform queries like this?
>
> I'm also slightly worried that the planar nature of the spatial
> indexes could prematurely remove points from the result set - is this
> the case?
>
> Will
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-- 
Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022