Consistent digital line segments
The authors introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms arising from Euclidean axioms. In particular, it is shown how to derive such a system of digital segments from any total order on the integers. As a consequence, the authors manage to define a system of digital segments such that all digital segments are, in the Hausdorff metric, optimally close to their corresponding Euclidean segments. Thus, an explicit construction is provided that solves the main question of \textit{J. Chun} et al. [Discrete Comput. Geom. 42, No. 3, 359--378 (2009; Zbl 1174.52008)].
scientific article; zbMATH DE number 6037504