Weighted Distances on the Trihexagonal Grid

Abstract

Recently chamfer distances have been developed not only on the usual integer grids, but also on some non traditional grids including grids which are not lattices. In this paper the trihexagonal grid is considered which is a kind of mix of the hexagonal and triangular grids: its pixels are hexagons and two shaped (oriented) triangles. Three types of 'natural' neighborhood relations are considered on the grid, consequently three weights are used to describe the chamfer distances. Formulae to compute the minimal weights of a connecting path, i.e., the distance of any two pixels, are provided to various cases depending on the relative ratio of the weights. Some properties of these distances, including metricity are also analysed.