[GRASS-user] Thiessen Polygons

[Jan Hartmann]

Yes, I guess that what I meant too, you just formulate it better, in a 
more general way. I find this interesting, as I have experimented with 
weighted Voronoi polygons, but only in vector format. There is a 
complete book on that methodolgy: Atsuyuki Okabe, Barry Boots, Kokochi 
Sugihara, Sung Nok Chiu: Spatial Tesselations. Concepts and Applications 
of Voronoi Diagrams. Wiley, Chichester 2000. It's really fascinating to 
see how much you can do with this technology, not only in theory but 
also in practice. Of course, the vector based algorithms are hard to 
implement and can be very resource hungry.  A lot of them are already 
available however: just Google on "weighted voronoi". As always, a 
raster based approach could be not only more efficient, but also 
conceptually more general. There is an ArcGIS extension available that 
does exactly this: see http://portal.acm.org/citation.cfm?id=1332465

With that in mind, if the algorithm you propose would be indeed an 
approximation to weighted Voronoi polygons, *and* it wouldn't be all to 
hard to implement (I have no idea about that), would it make sense to 
propose this as a new RFC for GRASS?

Jan

Glynn Clements wrote:
> Jan Hartmann wrote:
>
>   
>>> The problem with using r.cost is that you would need to know the cost
>>> for each cell before you have created the polygons.
>>>
>>> I think that the simplest accurate approach would be to modify
>>> r.grow.distance.
>>>       
>> Do you mean: adding a metric parameter to Euclidean, Squared, Manhattan, 
>> and Maximum? Something like: compute on the basis of the value of 
>> traversed cells?
>>     
>
> I mean scale the distance by the value of the nearest non-null cell.
>
>   
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