Shortest Paths in Triangular Grids with Neighbourhood Sequences

Abstract

In this paper we analyse some properties of the triangular and hexagonal grids in the 2D digital space. We define distances based on neighbourhood relations that can be introduced in these grids. We present an algorithm, which calculates the distance from an arbitrary point to another one for a given neighbourhood sequence in the triangular grid. Moreover, this algorithm produces a shortest path between these points, as well.