Design Nomenclature / Form & Geometry
Affine transform
Also called affine transformation, matrix transform, shear, translation, linear transform
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.