On the Chamfer Polygons on the Triangular Grid

Abstract

Weighted (or with other name, chamfer) distances on the triangular grid was introduced recently based on the three well-known neighborhoods. By having various values of the three used weights, the approximation of the Euclidean disks are shown, based on the isoperimetric ratio. Our results are also compared to similar results on the square grid. It is shown that the triangular grid, with three weights, overperforms the quality of the approximation on the square grid by both two and three weights (i.e., by the traditional 3 x 3 and the 5 x 5-neighborhoods, respectively) in terms of maximal and average relative errors.