Fundamentals of surface voxelization
Graphical Models and Image Processing
Computer Processing of Line-Drawing Images
ACM Computing Surveys (CSUR)
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
Circle digitization and cellular automata
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Defining Discrete Objects for Polygonalization: The Standard Model
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Another definition for digital tangents
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
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We study patterns that appear in discrete circles with integer center and radius. As the radius goes to infinity, the patterns get closer to digital straight segments: the notion of tangent words (described in Monteil DGCI 2011) allows to grasp their shape. Unexpectedly, some tangent convex words do not appear infinitely often due to deep arithmetical reasons related to an underlying Pell-Fermat equation. The aim of this paper is to provide a complete characterization of the patterns that appear in integer discrete circles for infinitely many radii.