Affine transformation

An affine transformation or affine map or an affinity (from the Latin, affinis, "connected with") between two vector spaces.

Physically, an affine transform is one that preserves

1. Colinearity between points, i.e., three points which lie on a line continue to be collinear after the transformation
2. Ratios of distances along a line, i.e., for distinct colinear points p_1, p_2, p_3, the ratio |p_2-p_1| / |p_3-p_2| is preserved

In general, an affine transform is composed of zero or more linear transformations (rotation, scaling or shear) and translation (shift). Several linear transformations can be combined into a single matrix.

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