Consistent digital rays (Q5896958)

A new definition of digital rays \(dig(op)\) from (fixed) origin \(o\) to a point \(p\) of the \(d\)-dimensional grid approximating the Eucludean line segment \(\overline{op}\) in Hausdorff metric and satisfying a set of Euclid-like axioms is suggested. The maximum Hausdorff distance between \(dig(op)\) and \(\overline{op}\) fits asymptotically \(\Theta(\log n)\) tight bound in \(n\times n\) grid. An application in image processing of star-shaped regions illustrates the theory.