Anonymous

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

- Colinearity between points, i.e., three points which lie on a line continue to be collinear after the transformation
- 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.

Anonymous

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