Given a Digital Straight Line (DSL) of known characteristics (
), we address the problem of computing the characteristics of any of its subsegments. We propose a new algorithm as a smart walk in the so called Farey Fan. We take profit of the fact that the Farey Fan of order
represents in a certain way all the digital segments of length
. The computation of the characteristics of a DSL subsegment is then equivalent to the localization of a point in the Farey Fan. Using fine arithmetical properties of the fan, we design a fast algorithm of theoretical complexity
is the length of the subsegment. Experiments show that our algorithm is faster than the one previously proposed by Said and Lachaud in [15,14] for “short” segments.