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I am working with an octree mesh where variables are stored in a collocated fashion at octant centers. I want to construct a lookup table for interpolation weights that may occur using only a cell and it's immediately adjacent neighbor leaf cells. There are a specific number of neighbor configurations since each neighbor is only allowed to be 1 level coarser or finer than the cell for which an interpolation is required, and I want to specify a unique table id for each configuration. Figure 4 in the paper below shows pretty clearly what I mean by surrounding cell configuration.

http://www.math.uh.edu/~molshan/ftp/pub/OctreeMAC.pdf

Is there an algorithm/accepted way to enumerate these cases?

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Your question is too terse to really understand what it is you're looking for. That said, the paper that you should look at is this one by Burstedde et al.: http://epubs.siam.org/doi/abs/10.1137/100791634 It describes the p4est library and has all sorts of algorithms to traverse octrees.

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  • $\begingroup$ I edited my question. I hope this makes it clear what I am asking. $\endgroup$
    – John Mousel
    Commented Apr 4, 2013 at 3:10

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