Weighted Distances on a Triangular Grid

Abstract

In this paper we introduce weighted distances on a triangular grid. Three types of neighborhood relations are used on the grid, and therefore three weights are used to define a distance function. Some properties of the weighted distances, including metrical properties are discussed. We also give algorithms that compute the weighted distance of any point-pair on a triangular grid. Formulae for computing the distance are also given. Therefore the introduced new distance functions are ready for application in image processing and other fields.