# [postgis-users] Amoeba Hulls

Stephen Woodbridge woodbri at swoodbridge.com
Wed Jul 5 12:38:01 PDT 2006

```Paul,

Would you not just connect the dots, like this.

1) determine the 80% points, say by distance or whatever
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
>>>>
>>>>
>>>>
>>>> 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: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.jsp?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?
>>>>      >      > be in a position to finance the development of this
>>>> feature.
>>>>      >      >
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>>>>
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