Finding shortest path with neighbourhood sequences in triangular grids

In this paper, we analyze some properties of triangular and hexagonal grids in 2D digital space. We define distances based on the neighbouring relations that can be introduced in these grids. On the triangular grid, this can be done by the help of neighbourhood sequences. We construct a shortest path in the hexagonal grid in a natural way. We present an algorithm, which produces, for a given neighbourhood sequence, a shortest path between two arbitrary points of the triangular grid, and also calculate the distance between these two points.