Digital distance in the kisrhombille grid with the edge neighborhood

Abstract

The kisrhombille tiling is the dual tessellation of one of the semi-regular tilings, composed of right-angled triangles arranged in 12 distinct orientations. A coordinate system has been employed to formally describe the grid of tiles. In this paper, two tiles are defined as neighbors if they share an edge in their boundary. The concept of digital distance is introduced as the minimum number of steps required to traverse between two tiles, and the corresponding distance formula is derived by constructing minimal paths.