[GRASS-user] Thiessen Polygons

[Moritz Lennert]

On 12/02/09 04:15, Dylan Beaudette wrote:
> On Wed, Feb 11, 2009 at 5:03 PM, Dylan Beaudette
> <debeaudette at ucdavis.edu> wrote:
>> On Wednesday 11 February 2009, MORREALE Jean Roc wrote:
>>> Hamish a écrit :
>>>> Kurt Springs wrote:
>>>>> Does anyone know how to do Thiessen Polygons in GRASS?
>>>>>
>>>>> I need to use them around various types of megalithic tomb
>>>>> sites that are in point vector files.
>>>> v.voronoi
>>>>
>>>>
>>>> there is some replacement test code to look at in grass-addons as well:
>>>>  http://trac.osgeo.org/grass/browser/grass-addons/vector/voronoi
>>> While we are on this topic, is there a way to get a weigthed voronoi
>>> diagram using grass ?
>>>
>>> The ability to rank a point to tune the area's influence would be great,
>>> for that purpose I've been using an arcgis'extension* but with grass it
>>> is not possible**. Is there a way to get a similar result ?
>>>
>>> *http://www.geog.unt.edu/~pdong/software.htm
>>> **http://osdir.com/ml/gis.grass.user/2004-04/msg00036.html
>>>
>>> Regards,
>>> MORREALE Jean Roc
> 
> Now that I have read about 'weighted voronoi diagrams', 

One version of such diagrams are Reilly surfaces [1],[2] used in retail 
geography to identify the influence/attraction zone of a city, often 
depending on population size.


> I wonder if a
> combination of r.cost + r.mapcalc would solve this problem. Something
> along those lines is demonstrated here:
> 
> http://casoilresource.lawr.ucdavis.edu/drupal/node/288
> 
> This example isn't quite what is requested, although using r.cost with
> start=point_i, and stop=neighbor_points (derived from v.delaunay /
> v.distance?) may work. It would then be a little more work to convert
> the weighted-distance rasters into polygons, and link back to the
> original attribute tables... but (hopefully) not outside the realm of
> possibility via a script.

This actually raises the same question as [3] about attributing pixels 
to closest neighbors (where "closest" can obviously be weighted). I 
think such a functionality would be very useful.

Moritz

[1] Reilly, W.J. (1929) Methods for the study of retail relationships, 
University of Texas, Bulletin, 2944.
[2] Reilly, W.J. (1931) The law of retail gravitation, New York.
[3] http://lists.osgeo.org/pipermail/grass-user/2009-January/048585.html