[postgis-users] Roeck test

[Burgholzer,Robert]

Would the following work (if max_distance were available, which it is
not in my distro)??:

SELECT ST_Buffer(centroid(the_geom), max_distance(centroid(the_geom),
the_geom) as bounding_circle ;

This assumes the following:
1. The Roeck test is essentially the "bounding circle" of a geometry
2. The centroid is the center of mass
3. the furtherest point from the center of mass will be enclosed by a
circle of radius equal to the distance from said point to the center
4. The max_distance function would work with points and multi-polygons

Thinking about a "bounding circle" makes me wonder: is this a useful
concept for geometric indexing?  Could this be used in conjunction with
the bounding box to create a more refined, quick and dirty bounding box
containment index?  In other words, if using the && operator essentially
throws out (or includes if NOT'ed) points outside a bounding box, would
it be computationally efficient to do something like a comparison to a
circle on the objects centroid?  In essence, all you would have to query
would be the centroid, and radius of the spheres, like (in pseudo-code):

If (distance(c1, c2) <= (r1 + r2)) then circles_overlap = true;
# where r1 and r2 are the radii of the two bounding circles, and c1 and
c2 are their centroids

With this simple comparison (maybe not so simple computationally, I
dunno), we could cut out a good deal of the blank space in the "corners"
of the bounding box.

Anyone?


Robert W. Burgholzer
Surface Water Modeler
Office of Water Supply and Planning
Virginia Department of Environmental Quality
rwburgholzer at deq.virginia.gov
804-698-4405
Open Source Modeling Tools:
http://sourceforge.net/projects/npsource/

-----Original Message-----
From: postgis-users-bounces at postgis.refractions.net
[mailto:postgis-users-bounces at postgis.refractions.net] On Behalf Of Lee
Meilleur
Sent: Friday, October 24, 2008 4:20 PM
To: 'PostGIS Users Discussion'
Subject: RE: [postgis-users] Roeck test


My bad, you're both correct.   If that's the case, what does the
ST_ExteriorRing function produce?  When I test it I get "geom is not a
polygon".


-----Original Message-----
From: postgis-users-bounces at postgis.refractions.net
[mailto:postgis-users-bounces at postgis.refractions.net] On Behalf Of Paul
Ramsey
Sent: Friday, October 24, 2008 2:59 PM
To: PostGIS Users Discussion
Subject: Re: [postgis-users] Roeck test


It's an inscribed circle? I thought it was a containing one.

P.

On Fri, Oct 24, 2008 at 12:50 PM, Lee Meilleur <lee.meilleur at gis.leg.mn>
wrote:
>
>
> The area of the convex hull is actually larger than the area of the
> polygon, so the ratio ends up being greater than 1.  With the Roeck
> test, the ratio will always be between 0 and 1, with a compact polygon
> approaching 1 (the area of the inner circle approaching the area of
> the polygon).  A ratio approaching 0 would indicate a gerrymandered
> district.
>
> Assuming my statement is correct that is:
>
> SELECT congress.district, area(ST_ConvexHull(congress.the_geom)) /
> area(congress.the_geom) AS convex_roeck FROM congress;
>
> Bruce, thanks for the idea, I'll see what I can produce from my
> minimal experience with stored procedures.
>
>
>
> -----Original Message-----
> From: postgis-users-bounces at postgis.refractions.net
> [mailto:postgis-users-bounces at postgis.refractions.net] On Behalf Of
Martin Davis
> Sent: Friday, October 24, 2008 11:40 AM
> To: PostGIS Users Discussion
> Subject: Re: [postgis-users] Roeck test
>
>
> Wouldn't it be easier and more accurate to use the convex hull of the
> polygon instead of the minimum enclosing ball? The CH will have
> smaller area (i.e. be a tighter bound on the area covered by the
> polygon), so it seems like it would give a more accurate basis for
> comparison.
>
> Lee Meilleur wrote:
>> Has anyone calculated the Roeck test using PostGIS?  This is an area
>> based measure that computes the ratio of the area of a polygon to the
>> area of the minimum enclosing circle for the polygon.  It's used to
>> measure compactness of districts for redistricting applications,
>> basically a way to test for gerrymandering.  Thanks.
>>
>> Lee Meilleur
>> LCC-GIS Office
>> Minnesota Legislature
>> 100 Rev. Dr. MLK Jr Blvd.
>> 55 State Office Building
>> St. Paul, MN 55155
>> 651.296.0098  Fax: 651.297.3697
>> lee.meilleur at gis.leg.mn
>> http://www.gis.leg.mn
>>
>>
>> _______________________________________________
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>>
>
> --
> Martin Davis
> Senior Technical Architect
> Refractions Research, Inc.
> (250) 383-3022
>
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