Theoretical Computer Science
Discrete linear objects in dimension n: the standard model
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
On an involution of Christoffel words and Sturmian morphisms
European Journal of Combinatorics
Offset Approach to Defining 3D Digital Lines
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Generation and recognition of digital planes using multi-dimensional continued fractions
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Minimal offsets that guarantee maximal or minimal connectivity of digital curves in nD
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Characterization of the closest discrete approximation of a line in the 3-dimensional space
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
A study of Jacobi-Perron boundary words for the generation of discrete planes
Theoretical Computer Science
On the structure of bispecial Sturmian words
Journal of Computer and System Sciences
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The aim of this paper is to discuss from an arithmetic and combinatorial viewpoint a simple algorithmic method of generation of discrete segments in the three-dimensional space. We consider discrete segments that connect the origin to a given point (u1, u2, u3) with coprime nonnegative integer coordinates. This generation method is based on generalized three-dimensional Euclid's algorithms acting on the triple (u1, u2, u3). We associate with the steps of the algorithm substitutions, that is, rules that replace letters by words, which allow us to generate the Freeman coding of a discrete segment. We introduce a dual viewpoint on these objects in order to measure the quality of approximation of these discrete segments with respect to the corresponding Euclidean segment. This viewpoint allows us to relate our discrete segments to finite patches that generate arithmetic discrete planes in a periodic way.