[GRASS-user] Thiessen Polygons

[Jan Hartmann]

Hamish wrote:
>  - use r.param.scale to create a feature map and extract all saddle-point
> boundaries between the bubbles as the voronoi boundaries,
> (or r.slope.aspect and find areas where slope<1 deg then r.thin, r.to.vect)
>
>
>   
Wouldn't this work with cost surfaces too? Starting from several points 
(the Thiessen centers) with a grid cell cost information raster 
containing only the value "one", you get a raster representation of a 
classic Thiessen structure. Manipulating the cost information raster , 
you should get something like a weighted Thiessen structure. The last 
step would be to extract the boundaries between the polygons in vector 
format, with the methods above. Starting from each center point, the 
cost surface will rise, until it meets the rising surface from an 
adjacent point. At this location, slope becomes zero. These zero slope 
areas are effectively the Thiessen polygons, and can be vectorized. For 
normal Thiessen polygons, this should be no problem, but I am not sure 
what happens with really complex weighted cases. Does anyone have any 
experience with this?

Jan