affine transformation

== English == === Noun === affine transformation (plural affine transformations) (geometry, linear algebra) A geometric transformation that preserves lines and parallelism, but in general not lengths or angles; (more formally) an automorphism of an affine space: a mapping of an affine space onto itself that preserves both the dimension of any affine subspace and the ratio of the lengths of any pair of parallel line segments. 2004, Solomon Khmelnik, Computer Arithmetic of Geometrical Figures: Algorithms and Hardware Design, Mathematics in Computer Comp., page 8, Most striking and well-known examples of affine transformation applications are computer tomography (see for instance [1]) and information compression for telecommunication systems (see [2]). This book describes affine transformations (displacements, turns, scaling, shifts) of n {\displaystyle n} -dimensional figures, where n = 1 , 2 , 3 , 4 {\displaystyle n=1,2,3,4} . ==== Synonyms ==== (geometric transformation that preserves lines and parallelism): affinity ==== Hypernyms ==== affine map, affine mapping, affine homomorphism (mappings from one space to a (generally) different one) ==== Hyponyms ==== linear transformation ==== Holonyms ==== affine group ==== Derived terms ==== affine transformation matrix ==== Translations ==== === Further reading === Geometric transformation on Wikipedia.Wikipedia Affine geometry on Wikipedia.Wikipedia Affine group on Wikipedia.Wikipedia Affine space on Wikipedia.Wikipedia Affine variety on Wikipedia.Wikipedia Complex affine space on Wikipedia.Wikipedia Anamorphosis on Wikipedia.Wikipedia Affine transformation on Encyclopedia of Mathematics