Characterization and generation of straight line segments on triangular cell grid

International audienceIn this paper we are considering straight lines and straight line segments defined by two triangle centroids in the triangular cell grid. A generation algorithm determining all the triangles (triangular cells) that are crossed by a straight line segment is proposed. There is the particular case where straight lines or straight line segments cross a vertex of the grid. We propose an arithmetical characterization of such lines and line segments