[postgis-users] Roeck test

[Bruce Rindahl]

Lee
I think a minimum enclosing circle might also be larger than the 
polygon.  Think of a circle circumscribing a square.  However I think 
you are right in needing a circle.  A district that is an elongated 
rectangle (could be a severely gerrymandered district) would have a 
ratio of 1 if the convex hull is used but a circle would have a much 
larger area.
Bruce


Lee Meilleur 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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