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?