Hexagonal indexing?
- To: mathgroup at smc.vnet.net
- Subject: [mg67675] Hexagonal indexing?
- From: AES <siegman at stanford.edu>
- Date: Tue, 4 Jul 2006 01:57:45 -0400 (EDT)
- Organization: Stanford University
- Sender: owner-wri-mathgroup at wolfram.com
Partly out of a practical problem, partly out of curiousity, are there
any standard conventions for "hexagonal indexing"? -- that is, for
attaching a single index k or a double index [m, n] to the points in
a planar hexagonal array so that one can conveniently do things like
--FInd the 6 nearest neighbors {m', n'] to a point [n, m] ?
--Find the coordinates of an arbitrary array point relative to an
optimally chosen origin or center?
--Find the distances between two array points [m', n] and [m", n"] ?
--Find all the array points on the outer rim of a finite hexagonal array
having 6 identical flat faces, or a finite hexagonal array maximally
filling a spherical shell?
--Efficiently convert the double indices (if used) to a single Mathematica
style array index?
I can surely work out some of these answers for myself, but I've never
encountered a "standard method" for doing these, and wonder if there is
an optimal or conventional approach?