J. Van-aken and M. Novak, Curve-drawing algorithms for Raster displays, ACM Transactions on Graphics, vol.4, issue.2, pp.147-169, 1985.
DOI : 10.1145/282918.282943

E. Andres, Discrete circles, rings and spheres, Computers & Graphics, vol.18, issue.5, pp.695-706, 1994.
DOI : 10.1016/0097-8493(94)90164-3

E. Andres, Modélisation Analytique Discrète d'Objets Géométriques. Habilitation à diriger des recherches, 2000.

E. Andres, Discrete linear objects in dimension n: the standard model, Graphical Models, vol.65, issue.1-3, pp.92-111, 2003.
DOI : 10.1016/S1524-0703(03)00004-3
URL : https://hal.archives-ouvertes.fr/hal-00354729

E. Andres, R. Acharya, and C. Sibata, Discrete analytical hyperplanes. CVGIP : Graphical Models and Image Processing, pp.302-309, 1997.
DOI : 10.1006/gmip.1997.0427

E. Andres and M. Jacob, The discrete analytical hyperspheres, IEEE Transactions on Visualization and Computer Graphics, vol.3, issue.1, pp.75-86, 1997.
DOI : 10.1109/2945.582354

E. Andres, C. Sibata, R. Acharya, and K. H. Shin, New methods in oblique slice generation, SPIE Medical Imaging'96 : Image Display, volume SPIE 2707, pp.580-589, 1996.

J. Bernoulli, Sur une nouvelle espèce de calcul, Recueil pour les Astronomes, pp.255-284

V. Berthé, C. Fiorio, and D. Jamet, Generalized Functionality for Arithmetic Discrete Planes, 12th International Conference On Didscrete Geometry for Computer Imagery, DGCI'05, pp.276-286, 2005.
DOI : 10.1007/978-3-540-31965-8_26

V. Berthé, C. Fiorio, D. Jamet, and F. Philippe, On some applications of generalized functionality for arithmetic discrete planes, Image and Vision Computing, vol.25, issue.10
DOI : 10.1016/j.imavis.2006.06.023

G. Bertrand, On p-simple points. Compte-Rendus de l'Académie des Sciences, Mathématique, issue.18, pp.3211077-1084, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00621996

G. Bertrand and R. Malgouyres, Some topological properties of discrete surfaces, DGCI, pp.325-336, 1996.
DOI : 10.1007/3-540-62005-2_28
URL : https://hal.archives-ouvertes.fr/hal-00622010

S. N. Biswas and B. B. Chaudhuri, On the generation of discrete circular objects and their properties, Computer Vision, Graphics, and Image Processing, vol.32, issue.2, pp.158-170, 1985.
DOI : 10.1016/S0734-189X(85)80066-9

]. J. Bresenham, Algorithm for computer control of a digital plotter, IBM Systems Journal, vol.4, issue.1, pp.25-30, 1965.
DOI : 10.1147/sj.41.0025

J. Bresenham, A linear algorithm for incremental digital display of cirucular arcs, Communications of the ACM, vol.20, issue.2, pp.100-106, 1977.
DOI : 10.1145/359423.359432

V. E. Brimkov, E. Andres, and R. P. Barneva, Object discretizations in higher dimensions, Pattern Recognition Letters, vol.23, issue.6, pp.623-636, 2002.
DOI : 10.1016/S0167-8655(01)00139-8

V. E. Brimkov and R. P. Barneva, Graceful planes and lines, Theoretical Computer Science, vol.283, issue.1, pp.151-170, 2002.
DOI : 10.1016/S0304-3975(01)00061-5
URL : http://doi.org/10.1016/s0304-3975(01)00061-5

V. E. Brimkov and R. P. Barneva, Connectivity of discrete planes, Theoretical Computer Science, vol.319, issue.1-3, pp.203-227, 2004.
DOI : 10.1016/j.tcs.2004.02.015

V. E. Brimkov, D. Coeurjolly, and R. Klette, Digital planarity???A review, Discrete Applied Mathematics, vol.155, issue.4, pp.468-495, 2007.
DOI : 10.1016/j.dam.2006.08.004
URL : https://hal.archives-ouvertes.fr/hal-00185059

V. E. Brimkov and R. Klette, Curves, Hypersurfaces, and Good Pairs of Adjacency Relations, IWCIA, pp.276-290, 2004.
DOI : 10.1007/978-3-540-30503-3_21

M. G. Castelli, F. Mignosi, and A. Restivo, Fine and Wilf's theorem for three periods and a generalization of Sturmian words, Theoretical Computer Science, vol.218, issue.1, pp.83-94, 1999.
DOI : 10.1016/S0304-3975(98)00251-5

J. M. Chassery and A. Montanvert, Geométrie discrète en analyse d'images. Hermès, 1991.

J. C. Ciria, A. De-miguel, E. Domínguez, A. R. Francés, and A. Quintero, A maximum set of (26, 6)-connected digital surfaces, IWCIA, pp.291-306, 2004.

D. Cohen-or and A. E. Kaufman, Fundamentals of surface voxelization. CVGIP : Graphical Model and Image Processing, pp.453-461, 1995.

M. Couprie and G. Bertrand, Simplicity surfaces : a new definition of surfaces in z 3, SPIE Vision Geometry V, pp.40-51, 1998.
URL : https://hal.archives-ouvertes.fr/hal-00622029

I. Debled-renesson, Etude et Reconnaissance des Droites et Plans Discrets, Thèse de doctorat, 1995.

I. Debled-rennesson, F. Feschet, and J. Rouyer-degli, Optimal blurred segments decomposition of noisy shapes in linear time, Computers & Graphics, vol.30, issue.1, pp.30-36, 2006.
DOI : 10.1016/j.cag.2005.10.007
URL : https://hal.archives-ouvertes.fr/inria-00173228

M. Doros, Algorithms for generation of discrete circles, rings, and disks, Computer Graphics and Image Processing, vol.10, issue.4, pp.366-371, 1979.
DOI : 10.1016/S0146-664X(79)80044-1

F. Feschet and J. Reveillès, A Generic Approach for n-Dimensional Digital Lines, DGCI, pp.29-40, 2006.
DOI : 10.1007/11907350_3

O. Figueiredo and J. Reveillès, A contribution to 3d digital lines, DGCI, pp.187-198, 1995.

O. Figueiredo and J. Reveillès, New results about 3d digital lines, SPIE Vision Geometry V, pp.98-108, 1996.

C. Fiorio, D. Jamet, and J. Toutant, Discrete circles : an arithmetical approach with nonconstant thickness, SPIE Electronic Imaging'06 : Vision Geometry XIV, pp.0-1, 2006.
DOI : 10.1117/12.642976
URL : https://hal.archives-ouvertes.fr/hal-00580556

C. Fiorio and J. Toutant, Arithmetic Discrete Hyperspheres and Separatingness, DGCI, pp.425-436, 2006.
DOI : 10.1007/11907350_36
URL : https://hal.archives-ouvertes.fr/lirmm-00128277

C. Fiorio and J. Toutant, Arithmetic characterization of polynomial-based discrete curves, Vision Geometry XV, 2007.
DOI : 10.1117/12.714475
URL : https://hal.archives-ouvertes.fr/lirmm-00186251

J. Françon, Sur la topologie d'un plan arithm??tique, Theoretical Computer Science, vol.156, issue.1-2, pp.159-176, 1996.
DOI : 10.1016/0304-3975(95)00059-3

H. Freeman, On the Encoding of Arbitrary Geometric Configurations, IEEE Transactions on Electronic Computers, vol.10, issue.2, pp.260-268, 1961.
DOI : 10.1109/TEC.1961.5219197

H. Freeman, Computer Processing of Line-Drawing Images, ACM Computing Surveys, vol.6, issue.1, pp.57-97, 1974.
DOI : 10.1145/356625.356627

Y. Gérard, Periodic graphs and connectivity of the rational digital hyperplanes, Theoretical Computer Science, vol.283, issue.1, pp.171-182, 2002.
DOI : 10.1016/S0304-3975(01)00063-9

F. C. Groen and P. W. Verbeek, Freeman-code probabilities of object boundary quantized contours, Computer Graphics and Image Processing, vol.7, issue.3, pp.391-400, 1978.
DOI : 10.1016/S0146-664X(78)80005-7

B. K. Horn, Circle generators for display devices, Computer Graphics and Image Processing, vol.5, issue.2, pp.280-288, 1976.
DOI : 10.1016/0146-664X(76)90036-8

S. H. Houng, On the Straightness of Digital Arcs, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.7, issue.2, pp.203-216, 1985.
DOI : 10.1109/TPAMI.1985.4767644

S. Y. Hsu, L. R. Chow, and H. C. Liu, A New Approach for the Generation of Circles, Computer Graphics Forum, vol.12, issue.2, pp.105-110, 1993.
DOI : 10.1111/1467-8659.1220105

D. Jamet, Géométrie Discrète : une Approche par la Combinatoire des Mots, Thèse de doctorat, 2005.

D. Jamet and J. Toutant, Minimal thickness connecting rational arithmetic discrete planes, Discrete Applied Mathematics

D. Jamet and J. Toutant, On the Connectedness of Rational Arithmetic Discrete Hyperplanes, DGCI, pp.223-234, 2006.
DOI : 10.1007/11907350_19
URL : https://hal.archives-ouvertes.fr/lirmm-00135621

B. W. Jordan-jr, W. J. Lennon, and B. D. Holm, An Improved Algorithm for the Generation of Nonparametric Curves, IEEE Transactions on Computers, vol.22, issue.12, pp.1052-1060, 1973.
DOI : 10.1109/T-C.1973.223650

C. E. Kim, Digital convexity, straightness, and convex polygons. Pattern Analysis and Machine Intelligence, pp.618-626, 1982.

C. E. Kim, Digital disks. Pattern Analysis and Machine Intelligence, pp.372-374, 1984.

C. E. Kim and T. A. Anderson, Digital disks and a digital compactness measure, Proceedings of the sixteenth annual ACM symposium on Theory of computing , STOC '84, pp.117-124, 1984.
DOI : 10.1145/800057.808673

R. Klette, The m-dimensional grid point space, Computer Vision, Graphics, and Image Processing, vol.30, issue.1, pp.1-12, 1985.
DOI : 10.1016/0734-189X(85)90014-3

R. Klette and A. Rosenfeld, Digital straightness???a review, Discrete Applied Mathematics, vol.139, issue.1-3, pp.197-230, 2004.
DOI : 10.1016/j.dam.2002.12.001

R. Klette, Multigrid Convergence of Geometric Features, Digital and Image Geometry, pp.318-338, 2000.
DOI : 10.1007/3-540-45576-0_19

T. Y. Kong, A. W. Roscoe, and A. Rosenfeld, Concepts of digital topology, Topology and its Applications, vol.46, issue.3, pp.219-262, 1992.
DOI : 10.1016/0166-8641(92)90016-S

T. Y. Kong and A. Rosenfeld, Digital topology : Introduction and survey, Computer Vision, Graphics, and Image Processing, pp.357-393, 1989.
DOI : 10.1016/0734-189x(89)90127-8

J. Koplowitz, On the Performance of Chain Codes for Quantization of Line Drawings, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.3, issue.2, pp.180-185, 1981.
DOI : 10.1109/TPAMI.1981.4767075

Z. Kulpa, On the properties of discrete circles, rings, and disks, Computer Graphics and Image Processing, vol.10, issue.4, pp.348-365, 1979.
DOI : 10.1016/S0146-664X(79)80043-X

Y. P. Kuzmin, An Efficient Circle-Drawing Algorithm, Computer Graphics Forum, vol.9, issue.4, pp.333-336, 1990.
DOI : 10.1109/TC.1979.1675240

C. Lincke and C. A. Wüthrich, Towards a unified approach between digitizations of linear objects and discrete analytical objects, WSCG, 2000.

C. Lincke and C. A. Wüthrich, Surface digitizations by dilations which are tunnel-free, Discrete Applied Mathematics, vol.125, issue.1, pp.81-91, 2003.
DOI : 10.1016/S0166-218X(02)00225-1
URL : http://dx.doi.org/10.1016/s0166-218x(02)00225-1

R. Malgouyres, There is no local characterization of separating and thin objects in Z3, Theoretical Computer Science, vol.163, issue.1-2, pp.303-308, 1996.
DOI : 10.1016/0304-3975(96)00021-7

R. Malgouyres, A definition of surfaces of Z3 A new 3D discrete Jordan theorem, Theoretical Computer Science, vol.186, issue.1-2, pp.1-41, 1997.
DOI : 10.1016/S0304-3975(96)00213-7

R. Malgouyres, Local characterization of strong surfaces within strongly separating objects, Pattern Recognition Letters, vol.19, issue.3-4, pp.341-349, 1998.
DOI : 10.1016/S0167-8655(97)00174-8

R. Malgouyres and G. Bertrand, A new local property of strong n-surfaces, Pattern Recognition Letters, vol.20, issue.4, pp.417-428, 1999.
DOI : 10.1016/S0167-8655(99)00010-0
URL : https://hal.archives-ouvertes.fr/hal-00622103

M. D. Mcilroy, Best approximate circles on integer grids, ACM Transactions on Graphics, vol.2, issue.4, pp.237-263, 1983.
DOI : 10.1145/245.246

D. G. Morgenthaler and A. Rosenfeld, Surfaces in three-dimensional digital images, Information and Control, vol.51, issue.3, pp.227-247, 1981.
DOI : 10.1016/S0019-9958(81)90290-4

M. Morse and G. A. Hedlund, Symbolic Dynamics II. Sturmian Trajectories, American Journal of Mathematics, vol.62, issue.1/4, pp.1-42, 1940.
DOI : 10.2307/2371431

S. Pham, Digital circles with non-lattice point centers. The Visual Computer, pp.1-24, 1992.
DOI : 10.1007/bf01901025

M. L. Pitteway, Algorithm for drawing ellipses or hyperbolae with a digital plotter, The Computer Journal, vol.10, issue.3, pp.282-289, 1967.
DOI : 10.1093/comjnl/10.3.282

M. L. Pitteway, ???Integer Circles, Etc.??? ??? some further thoughts, Computer Graphics and Image Processing, vol.3, issue.3, pp.262-265, 1974.
DOI : 10.1016/0146-664X(74)90020-3

M. L. Pitteway, ???Integer Circles, Etc.??? - three move extension of Bresenham's algorithm, Computer Graphics and Image Processing, vol.3, issue.3, pp.260-261, 1974.
DOI : 10.1016/0146-664X(74)90019-7

J. Reveillès, Géométrie discrète, calcul en nombres entiers et algorithmique, Thèse d'Etat, 1991.

C. Ronse and M. Tajine, Discretization in hausdorff space, Journal of Mathematical Imaging and Vision, vol.12, issue.3, pp.219-242, 2000.
DOI : 10.1023/A:1008366032284

C. Ronse and M. Tajine, Hausdorff Discretization for Cellular Distances and Its Relation to Coverand Supercover Discretizations, Journal of Visual Communication and Image Representation, vol.12, issue.2, pp.169-200, 2001.
DOI : 10.1006/jvci.2000.0458

A. Rosenfeld, Arcs and Curves in Digital Pictures, Journal of the ACM, vol.20, issue.1, pp.81-87, 1973.
DOI : 10.1145/321738.321745

A. Rosenfeld, Digital Straight Line Segments, IEEE Transactions on Computers, vol.23, issue.12, pp.1264-1369, 1974.
DOI : 10.1109/T-C.1974.223845

A. Rosenfeld, A converse to the Jordan curve theorem for digital curves, Information and Control, vol.29, issue.3, pp.292-293, 1975.
DOI : 10.1016/S0019-9958(75)90459-3

H. Sánchez-cruz, E. Bribiesca, and R. M. Rodríguez-dagnino, Efficiency of chain codes to represent binary objects, Pattern Recognition, vol.40, issue.6, pp.1660-1674, 2007.
DOI : 10.1016/j.patcog.2006.10.013

F. Schweiger, Multidimensional Continued Fractions, 2000.

M. Tajine and C. Ronse, Topological properties of Hausdorff discretization, and comparison to other discretization schemes, Theoretical Computer Science, vol.283, issue.1, pp.243-268, 2002.
DOI : 10.1016/S0304-3975(01)00082-2

M. Tajine, D. Wagner, and C. Ronse, Hausdorff Discretization and Its Comparison to Other Discretization Schemes, DGCI, pp.399-412, 1999.
DOI : 10.1007/3-540-49126-0_31

J. Toutant, Characterization of the Closest Discrete Approximation of a Line in the 3-Dimensional Space, pp.618-627, 2006.
DOI : 10.1007/11919476_62
URL : https://hal.archives-ouvertes.fr/lirmm-00135626

L. Vuillon, X. Wu, and J. G. Rokne, Local configurations in a discrete plane Double-step incremental generation of lines and circles, Bulletin of the Belgian Mathematical Society Computer Vision, Graphics, and Image Processing, vol.6, issue.373, pp.625-636331, 1987.

C. A. Wüthrich, A model for curve rasterization in n-dimensional space, Computers & Graphics, vol.22, issue.2-3, pp.153-160, 1998.
DOI : 10.1016/S0097-8493(98)00001-6

C. Yao and J. G. Rokne, Hybrid scan-conversion of circles, IEEE Transactions on Visualization and Computer Graphics, vol.1, issue.4, pp.311-318, 1995.