A rational rotation method for robust geometric algorithms
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Rotated dispersed dither: a new technique for digital halftoning
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Three-dimensional rotations by three shears
Graphical Models and Image Processing
Regular Article: Cellular Automaton Growth on Z2: Theorems, Examples, and Problems
Advances in Applied Mathematics
Journal of Computational Physics
Discrete parabolas and circles on 2D cellular automata
Theoretical Computer Science - Special issue on Caen '97
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Cellular Automata: A Discrete Universe
Cellular Automata: A Discrete Universe
Finite-resolution computational geometry
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Characterization of bijective discretized rotations
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Fast image transforms using diophantine methods
IEEE Transactions on Image Processing
Hinge Angles for 3D Discrete Rotations
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Self-similar discrete rotation configurations and interlaced Sturmian words
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Incremental and transitive discrete rotations
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Sufficient conditions for topological invariance of 2d images under rigid transformations
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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A discretized rotation acts on a pixel grid: the edges of the neighborhood relation are affected in particular way. Two types of configurations (i.e. applications from Z^2 to a finite set of states) are introduced to code locally the transformations of the neighborhood. All the characteristics of discretized rotations are encoded within the configurations. We prove that their structure is linked to a subgroup of the bidimensional torus. Using this link, we obtain a characterization of periodical configurations and we prove their quasi-periodicity for any angle.