Definition of "affine transformation" noun 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 . quotations examples

Quotations Just as for plane transformations , we may show that the set of all affine transformations of space form a group .Under an affine transformation of space , the image of a line is a line , and the image of a plane is a plane .

1965, P. S. Modenov, A. S. Parkhomenko, translated by Michael B. P. Slater, Geometric Transformations, Volume 1: Euclidean and Affine Transformations, Academic Press, page 145

Most striking and well -known examples of affine transformation applications are computer tomography (see for instance ) and information compression for telecommunication systems (see ). / 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} .

2004, Solomon Khmelnik, Computer Arithmetic of Geometrical Figures: Algorithms and Hardware Design, Mathematics in Computer Comp., page 8