Re: [Repast-developer] Figurate Numbers, Neighborhoods and Distances.

[Thomas H. <th...@tr...>]

Those both seem fine.  Keep in mind, though, that those only describe how to do range queries.  Distance queries are a bit different.  A distance query in a Moore neighborhood can be done fairly easily using one of the many graphics line drawing algorithms.  This will be more difficult (I think, but I'm not quite sure) to determine in the VonNeumannTopology.  So we should figure out how to caluculate those distances.

One particularly nice thing about those references, though is that it gives us a reference to use to name our topology lib (perhaps).  See:

http://mathworld.wolfram.com/Neighborhood.html

-Tom

On Sat, Jun 28, 2003 at 01:16:55PM -0400, Mark R. Diggory wrote:
> I've been considering how to deal with the concept of "Distance" in 
> Neighborhood topologies. Ideally, I think distance is commensurate on 
> the concept of "spatial structure", in other words, resolving a distance 
> in the "discrete" VN neighborhood,  Moore neighborhood and Hex 
> neighborhood will all yield different values based on the neighborhood 
> rules defining that space
> 
> for example:
> 
> in VN space the distance is determined by the equation at the bottom of 
> this page:
> http://mathworld.wolfram.com/vonNeumannNeighborhood.html
> 
> Moore is simpler:
> http://mathworld.wolfram.com/MooreNeighborhood.html
> 
> The Hexagonal distance is based on "even/odd" y values of the origin 
> (x1,y1), its a combination of these two above measures if for even rows 
> if x1 > x2 calc VN distance, if x1 <= x2 calc Moore distance. this 
> inverts for odd rows.
> 
> This is all opposed to the idea of using the euclidean distance which 
> would be more accurate for continuous real spaces which will probably be 
> found in GIS systems.
> 
> What do you think?
> Mark
> 
> 
> 
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