I have DEM raster data of an island and I have 10 points (cities).
My task is to map the island into areas. Inside these areas everything must be nearest to the corresponding city/point, and each area must be delimited against neighboring areas where other cities are nearest. So in principle it is similar to a voronoi calculation.
The difference from a classic voronoi is that these areas must be calculated "3-dimensionally", meaning they must be defined using costs respecting how long it would take to get around the cities regarding all slopes.
Thus, e.g. a city inside mountains must result in a much smaller area than a city in flatlands (because it takes longer/has higher costs moving over the mountains than over flat land).
Of course I will need a cost analysis in GRASS in the first place. But what tools/plugins can I use to calculate the "3D-Voronoi-part" to generate my delimited areas map using this cost data?
I hope I made clear what I need to figure out how to do.