Affine Transformation: Vector space, Affine space, Geometry, Linear map, Euclidean space, Rotation (mathematics), Shear mapping, Transformation ... Homothetic transformation, 3D projection. Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis, 'connected with') between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation:x mapsto A x+ b.In the finite-dimensional case each affine transformation is given by a matrix A and a vector b, satisfying certain properties described below.Geometrically, an affine transformation in Euclidean space is one that preserves VDM Publishing House. Paperback. Condizione libro: new. BRAND NEW PRINT ON DEMAND., Affine Transformation, Frederic P. Miller, Agnes F. Vandome, John McBrewster. Source.