Number of shortest paths in triangular grid for 1- and 2-neighborhoods

Abstract

This paper presents a novel formulation to determine the number of shortest paths between two points in triangular grid in 2D digital space. Three types of neighborhood relations are used on the triangular grid. Here, we present the solution of the above mentioned problem for two neighborhoods—1-neighborhood and 2-neighborhood. To solve the stated problem we need the coordinate triplets of the two points. This problem has theoretical aspects and practical importance. © Springer International Publishing Switzerland 2015.