affine function

In geometry, an affine transformation, or an affinity (from the Latin, affinis, "connected with") is an automorphism of an affine space. More specifically, it is a function mapping an affine space onto itself that preserves the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and also preserves the ratio of the lengths of parallel line segments. Consequently, sets of parallel affine subspaces remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line. https://en.wikipedia.org/wiki/Affine_transformation