1.NounA geometric transformation that preserves lines and parallelism, but in general not lengths or angles; 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."An affine transformation does not in general preserve angles between lines or distances between points, but it does preserve ratios of distances between points lying on a straight line.; Given an affine space
X
{\displaystyle X}
, every affine transformation on
X
{\displaystyle X}
can be represented as the composition of a linear transformation on
X
{\displaystyle X}
and a translation of
X
{\displaystyle X}
.; Examples of affine transformations include translation, scaling, homothety, similarity, reflection, rotation, shear and compositions of them in any combination and sequence."