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A quasi-affine transformation, being the whole part of a rational affine transformation, is the discretized form of an affine transformation. Introduced by Marie-André Jacob-Da Col, it has been the subject of numerous studies. This article is devoted to the study of the algebraic structures of some quasi-affine bijective transformations, in particular the discrete translations of isolated points and Pythagorean rotations.
Andres E, Jacob-Da Col MA. Discrete affine transformations”, In: D. Coeurjolly, A. Montanvert and J. Chassery (Eds.), Discrete geometry and digital images, Paris: Lavoisier. 2007;173-190.
Jacob-Da Col MA. Quasi-affine applications and tilings of the discrete plane,” Theoretical Computer Science. 2011;259(11-2):245-269.
Blot V, Coeujolly D. Quasi-affine Transformation in Higher dimension,” 15th International Conference on Discrete Geometry for Computer Imagery, LNCS, Montreal; 2009.
Pluta K, Romon P, Kenmochi Y, Passat N. Bijective digitized rigid motions on subsets of the plane Journal of Mathematical Imaging and Vision. 2017;59:84–105. Available:https://doi.org/10.1007/s10851-017-0706-8.
Mbuyi Kalubi C, Musesa Landa A. On Affine transformations in continuous and in discrete spaces,” Congo sciences. 2020;1-8.
Kim C. Three-dimensional digital planes,” IIEEE Transactions on Pattern Analysis and Machine Intelligence. 1984;6(15):639-645.
Nehlig P. Quasi-affine transformation: tilings by reciprocal images,” Theorical Computer Science. 1995;156:1-38.
Jacob-Da Col MA. Applications quasi-affines”, Ph.D. Thesis, University Louis Pasteur, Strasbourg; 1993.
Jacob-Da co MA, P Tellier. Quasi-linear transformations and discrete tilings,” Theoretical Computer Science. 2009;410:2126-2134.
Arnaudiès J, Fraysse H. Mathematics Course 1-Algebra, Paris: Bordas; 1982.