affine transformation

Definitions

1. 1

   A geometric transformation that preserves lines and parallelism, but in general not…

   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.

   • 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, every affine transformation on X can be represented as the composition of a linear transformation on X and a translation of X.
   • Examples of affine transformations include translation, scaling, homothety, similarity, reflection, rotation, shear and compositions of them in any combination and sequence.

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