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

[Mark R. D. <mdi...@la...>]

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