Weighted Distances Based on Neighbourhood Sequences in Non-standard Three-Dimensional Grids

By combining weighted distances and distances based on neighbourhood sequences, a new family of distance functions with potentially low rotational dependency is obtained. The basic theory for these distance functions, including functional form of the distance between two points, is presented for the face-centered cubic grid and the body-centered cubic grid. By minimizing an error function, the optimal combination of weights and neighbourhood sequence is derived.