[postgis-users] Amoeba Hulls

Wed Jul 5 15:16:54 PDT 2006

Maybe:

1: Find distance to 80% of customers via network analysis.

2: Use that distance to find all points along network at that distance

3: Form polygon from points in 2

Bruce

  _____  

From: postgis-users-bounces at postgis.refractions.net
[mailto:postgis-users-bounces at postgis.refractions.net] On Behalf Of
Josh at oklieb
Sent: Wednesday, July 05, 2006 4:07 PM
To: PostGIS Discussion
Subject: Re: [postgis-users] Amoeba Hulls

Notice that the boundary in the supplied figure curves even in the absence
of any controlling points. That usually means to me that there is a surface
function at work and the line is a contour, here containing 80% of the
customer "volume". I know that I've used geostatistics modules in Arcview 3
(way back when) and this may be a similar approach.

Josh Lieberman

On Jul 5, 2006, at 4:40 PM, Bruce Rindahl wrote:

Will

Did you create this using ArcView 3.x Business Analyst? If so, the Avenue
code is available from that interface. That could give us a guide on how it
was created.

Bruce Rindahl

  _____  

From: postgis-users-bounces at postgis.refractions.net
[mailto:postgis-users-bounces at postgis.refractions.net] On Behalf Of William
Andersen
Sent: Wednesday, July 05, 2006 2:15 PM
To: PostGIS Users Discussion
Subject: Re: [postgis-users] Amoeba Hulls

Steve,

I think you are onto something.

There are exactly 101 points in each of the polygons in the (small) sample
set that I have.

When i get a little more time i'll plot these with 3.6 degree wedges and see
if anything jumps out at me. 

My working theory is that there are a set of rules determining what happens
at each control point. In some cases it's pretty simple as we have enough
points to pick one that includes the 80% points but not the 20% points. In
other cases it seems to be extrapolated from the neighboring points using
some kind of fitted curve. 

Will

On 7/5/06, Stephen Woodbridge <woodbri at swoodbridge.com> wrote:

Paul,

Would you not just connect the dots, like this.

1) determine the 80% points, say by distance or whatever
2) order the points by radial angle increasing and radius decreasing
3) use something like a window say plus/minus 1/2 degree and select the 
maximum radius in the window and add that point to the polygon
4) step 1/2 degree and repeat 3)
5) close the polygon

You probably need to have some special handling if there is a sudden
change in radius to make sure no points get clicked out of the polygon. 

Anyway I think this would be a good start to the algorithm.

-Steve

Paul Ramsey wrote:
> Indeed, nice to see that everything can be strung together. I am trying
> to visualize what a "squishyhull" function would have to do to work 
> though :) It's a not uncommon request... the calculated equivalent of
> someone squinting and drawing a line around a group of points.
>
> P
>
> Mike Leahy wrote:
>> Hey there, 
>>
>> If you can determine the closest 80% of points by whatever criteria,
>> wouldn't you be able to use the convexhull() function? I just tried
>> this, and it looks okay to me:
>>
>> testdb=# select astext(convexhull('MULTIPOINT((0 1),(0 0),(1 0),(1
>> 1))'::geometry));
>> astext
>> --------------------------------
>> POLYGON((0 0,0 1,1 1,1 0,0 0)) 
>> (1 row)
>>
>> I did the same thing after creating a points table with the separate
>> in individual records with the same overall coordinates in the
>> multipoint example above, and it worked okay too: 
>>
>> testdb=# select astext(convexhull(collect(p))) from testpoint;
>> astext
>> --------------------------------
>> POLYGON((0 0,0 1,1 1,1 0,0 0))
>> (1 row) 
>>
>> It wouldn't be too hard to modify this to work using where condition
>> that filters out the records of interest...or maybe on a saved view.
>>
>> The only problem is that it wouldn't produce a nice curvy polygon 
>> outline like in the sample William provided.
>>
>> Regards,
>> Mike
>>
>> Paul Ramsey wrote:
>>> So my guess is that you use drive-time to segment your population of 
>>> customers relative to the store into the "nearest X%" and then draw a
>>> "shape" around that cloud of points. And drawing the shape is the
>>> "fun" part. 
>>>
>>> William Andersen wrote:
>>>> It appears to be the same as this functionality in Business Analyst
>>>>
>>>>
http://www.esri.com/software/arcgis/extensions/businessanalyst/about/custome
r-market.html
>>>>
<http://www.esri.com/software/arcgis/extensions/businessanalyst/about/custom
er-market.html >
>>>>
>>>>
>>>> I thought this was done using some older version of Arcview, but i'm
>>>> not very familiar with esri's offerings.
>>>>
>>>> Will
>>>>
>>>> On 7/5/06, *Paul Ramsey * <pramsey at refractions.net
>>>> <mailto: <mailto:pramsey at refractions.net>  pramsey at refractions.net>>
wrote:
>>>>
>>>> This wouldn't be in vanilla arcview, was it in Network Analyst?
>>>> The top
>>>> 80% of points by drive distance might yield this shape. Finding 
>>>> the
>>>> points would be straightforward, and then the hull building
>>>> would be the
>>>> hand-waving part.
>>>>
>>>> P 
>>>>
>>>> William Andersen wrote:
>>>> > Paul, Steve,
>>>> >
>>>> > Thanks for the quick replies, unfortunately it's pretty hard 
>>>> to tell
>>>> > from those images if they match.
>>>> >
>>>> > I've done some more digging and it turns out that these
>>>> shapes were 
>>>> > created in Arcview 3.x. The notes I have say...
>>>> >
>>>> > > This approach selects a number of the outliers and joins the
>>>> extreme 
>>>> > points using elliptical arcs.
>>>> > > The arcs are all created in a direction moving out from the
>>>> store.
>>>> >
>>>> > However, I dont see customer points at the discontinuities in
>>>> the
>>>> hulls,
>>>> > so it appears that the "extreme points" are perhaps 
>>>> interpolated.
>>>> >
>>>> >
>>>> > Will
>>>> >
>>>> > On 7/5/06, *Paul Ramsey* < pramsey at refractions.net
>>>> <mailto:pramsey at refractions.net>
>>>> > <mailto:pramsey at refractions.net 
>>>> <mailto:pramsey at refractions.net>>> wrote:
>>>> >
>>>> > William,
>>>> > 
>>>> > It doesn't look like this is a standard algorithm, but more
>>>> likely a
>>>> > particular empirical technique provided by the particular
>>>> software you
>>>> > were using. So substituting some other technique might
>>>> yield a
>>>> > different shape entirely... do any of the techniques 
>>>> mentioned here
>>>> >
>>>>
<http://www.geospatial-online.com/geospatialsolutions/article/articleDetail.
jsp?id=1348 
>>>>
>>>> > <
>>>>
>>>>
http://www.geospatial-online.com/geospatialsolutions/article/articleDetail.j
sp?id=1348 >>
>>>>
>>>> > sound like what was done to your data?
>>>> >
>>>> > Paul
>>>> >
>>>> > William Andersen wrote: 
>>>> > >
>>>> > > I'm fairly new to postgis, and working to automate a
>>>> number of
>>>> > > processes.
>>>> > > 
>>>> > > We are trying to compute market area polygons that look
>>>> like the
>>>> > > attached image. These were created by some older
>>>> software.
>>>> > >
>>>> > >
>>>> > > They are referred to as Amoeba Hulls, and they contain
>>>> 80% 
>>>> of a
>>>> > > store's customers. However I can't find any solid
>>>> documentation that
>>>> > > would allow me to reproduce them. 
>>>> > >
>>>> > > Does anyone have any ideas how these shapes are
>>>> created or an
>>>> > > alternate name that I might be able to google? 
>>>> Additionally, we may
>>>> > > be in a position to finance the development of this
>>>> feature.
>>>> > >
>>>> > _______________________________________________ 
>>>> > postgis-users mailing list
>>>> > postgis-users at postgis.refractions.net
>>>> <mailto: postgis-users at postgis.refractions.net>
>>>> > <mailto:postgis-users at postgis.refractions.net 
>>>> <mailto:postgis-users at postgis.refractions.net>>
>>>> >
>>>> http://postgis.refractions.net/mailman/listinfo/postgis-users
>>>> >
>>>> >
>>>> >
>>>> >
>>>>
>>>>
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