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Hey Robert!<br>
I have been thinking about this because I also have an application that
could use the minimum bounding circle. Unfortunately your idea would
not work. Picture the following counter example:<br>
Start with a square. The centroid is in the center and you idea would
work fine. Now take a small segment of the top side and expand it like
a triangle upward. It will look like a little text box or cartoon
speech bubble. Now expand that little triangle a long distance away
from the square but keep it thin. The centroid of the shape will still
be dominated by the area of the square but your circle will go through
the far vertex. You can see the circle will be far greater than it
needs to be. If your shape is symmetrical, the minimum bounding circle
will run through the two bottom corners and the top expanded vertex.<br>
I want to try to get a procedure done based on the previous links and
test it. If it works and there is a demand I could write a patch.<br>
<br>
Bruce<br>
<br>
<br>
Burgholzer,Robert wrote:
<blockquote
cite="mid:6C097DA58429B743A67070F98BE73A370379B6E8@deqex01.deq.local"
type="cite">
<pre wrap="">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
<a<a class="moz-txt-link-rfc2396E" href="mailto:oftheboundingbox.Anyone?RobertW.BurgholzerSurfaceWaterModelerOfficeofWaterSupplyandPlanningVirginiaDepartmentofEnvironmentalQualityrwburgholzer@deq.virginia.gov804-698-4405OpenSourceModelingTools:http://sourceforge.net/projects/npsource/-----OriginalMessage-----From:postgis-users-bounces@postgis.refractions.net[mailto:postgis-users-bounces@postgis.refractions.net]OnBehalfOfLeeMeilleurSent:Friday,October24,20084:20PMTo:'PostGISUsersDiscussion'Subject:RE:[postgis-users]RoecktestMybad,you'rebothcorrect.Ifthat'sthecase,whatdoestheST_ExteriorRingfunctionproduce?WhenItestitIget">"
of the bounding box.
Anyone?
Robert W. Burgholzer
Surface Water Modeler
Office of Water Supply and Planning
Virginia Department of Environmental Quality
rwburgholzer@deq.virginia.gov
804-698-4405
Open Source Modeling Tools:
http://sourceforge.net/projects/npsource/
-----Original Message-----
From: postgis-users-bounces@postgis.refractions.net
[mailto:postgis-users-bounces@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 "</a>geom is not a
polygon".
-----Original Message-----
From: <a class="moz-txt-link-abbreviated" href="mailto:postgis-users-bounces@postgis.refractions.net">postgis-users-bounces@postgis.refractions.net</a>
[<a class="moz-txt-link-freetext" href="mailto:postgis-users-bounces@postgis.refractions.net">mailto:postgis-users-bounces@postgis.refractions.net</a>] 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 <a class="moz-txt-link-rfc2396E" href="mailto:lee.meilleur@gis.leg.mn"><lee.meilleur@gis.leg.mn></a>
wrote:
</pre>
<blockquote type="cite">
<pre wrap="">
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: <a class="moz-txt-link-abbreviated" href="mailto:postgis-users-bounces@postgis.refractions.net">postgis-users-bounces@postgis.refractions.net</a>
[<a class="moz-txt-link-freetext" href="mailto:postgis-users-bounces@postgis.refractions.net">mailto:postgis-users-bounces@postgis.refractions.net</a>] On Behalf Of
</pre>
</blockquote>
<pre wrap=""><!---->Martin Davis
</pre>
<blockquote type="cite">
<pre wrap="">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:
</pre>
<blockquote type="cite">
<pre wrap="">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
<a class="moz-txt-link-abbreviated" href="mailto:lee.meilleur@gis.leg.mn">lee.meilleur@gis.leg.mn</a>
<a class="moz-txt-link-freetext" href="http://www.gis.leg.mn">http://www.gis.leg.mn</a>
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</pre>
</blockquote>
<pre wrap="">--
Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022
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