Digital disks by weighted distances in the triangular grid

Abstract

Weighted (or with other name, chamfer) distances on the triangular grid was introduced recently based on the three possible neighborhood. In this paper, digital disks are defined and analyzed based on these weighted distances: geometric and combinatorial properties are studied. Approximation of the Euclidean circles and distances are shown. The obtained disks are usually dodecagons, enneagons (nonagons) or hexagons. They are proven to be digitally convex. © Springer International Publishing Switzerland 2016.