Abstract
Given a Digital Straight Line (DSL) of known characteristics (a,b,μ), 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 n represents in a certain way all the digital segments of length n. 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 where n 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. © 2013 Springer-Verlag Berlin Heidelberg.
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CITATION STYLE
Sivignon, I. (2013). Walking in the farey fan to compute the characteristics of a discrete straight line subsegment. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7749 LNCS, pp. 23–34). Springer Verlag. https://doi.org/10.1007/978-3-642-37067-0_3
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