Glynn Clements wrote:
Jan Hartmann wrote:
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?
Oops; I spoke too soon.
In retrospect, this won't work. r.grow.distance relies upon the fact
that once a cell falls out of consideration, it stays out. It will
only consider cells which either are from the current row, or were
used on the previous row.
With distance scaling, this doesn't hold. A cell could be temporarily
overriden by much nearer cells with increased scale factors (lower
weights), then regain its influence once the distance increases.
IOW, this isn't something which can implemented given the algorithm
used by r.grow.distance. Any algorithm which implemented distance
scaling would inevitably have worst-case memory usage proportional to
the number of non-null input cells, as you can never "forget" a cell
whose scale factor is lower than those currently being considered, as
it will eventually regain its influence.
Do you mean that implementing a raster version of weighted Voronoi
methods would be very inefficient, compared to vector methods, or that
it would be very difficult? I have tried to see what's in the ArcGIS
extension (http://portal.acm.org/citation.cfm?id=1332465, documentation
at: http://www.geog.unt.edu/~pdong/software/VoronoiHelp.pdf), but the
math is beyond me. If you think it would be viable to implement this in
GRASS, I could have a closer look at it. These weighted Voronoi polygons
are really an interesting methodology.
Jan Hartmann
Departmann of Geography
University of Amsterdam
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