affine transform

A linear map plus a translation -- preserves parallel lines but not necessarily angles or lengths.

An affine transform combines a linear map (rotation, scaling, shear) with a translation, and in homogeneous-coordinate matrix form always has bottom row $[0,\,0,\,1]$ . Affine transforms preserve parallel lines and ratios of lengths along a line, but not angles or lengths in general.

Examples

Shearing and translating a square keeps its opposite sides parallel, but a photographed square viewed at a steep angle is no longer describable by an affine transform alone.