Re: constructing an N dimensional grid/mesh.

Amit Bhatia <amit.bhatia@xxxxxxxxx> wrote:
> Hello,
> I am trying to make an N dimensional grid of identical cells, wherein
> given an element it is easy to find other elements that share one or
> more edges with it.

You'll want to clarify what you mean by "edges". Cells boundaries are
edges only for N=2. For N=3 they're rectangles, in higher dimensions
they're (N-2) dimensional "hyper-rectangles". Cells may share only
intersections of such N-2 dimensional boundaries (vertices, edges,
faces, ... (N-3) dimensional rectangles). I hope you didn't really
mean to restrict the definition of "neighbor" to those cells that
share exactly 1-dimensional edges, did you?

> Any suggestions on how it could be done: in 2 dimensions, it is
> relatively straightforward, but in general N dimensional euclidean
> space I can't think of a way of doing it.

I don't see what's so hard about it: a cell is identified by an
N-element tuple of indices. Its direct neighbors are all cells that
differ by one count in exacly one index. It's lesser neighbors are
all cells that differ by at most one count in each index.

--
Hans-Bernhard Broeker (broeker@xxxxxxxxxxxxxxxxxxxxx)
Even if all the snow were burnt, ashes would remain.
.

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