Design Nomenclature / Form & Geometry
Affine transform
Also called affine transformation, matrix transform, shear, translation, linear transform
This entry has not been translated yet and is shown in English.
Any map preserving straight lines, parallelism, and ratios of lengths along a line, but not necessarily length or angle: translation, rotation, uniform and non-uniform scale, shear, reflection, and any composition of them. Written as a matrix plus a translation, or as one 4×4 in homogeneous coordinates — which is why the graphics stack works in four dimensions.
In practice
Order matters: rotate-then-translate is not translate-then-rotate, and every 'why did it fly off into space' is a composition-order problem. Perspective is the common transform that is not affine — it does not preserve parallels, which is the whole point of it.