The term “Affine” was coined by Euler (1748b), motivated by the idea that images related by affine transformation have an affinity with one another.
Note 1: The term “Affine Geometry” is never used in GCE A-level Math, but commonly taught in French Baccalaureate.
Note 2: “Affinity” 亲和力 => 模仿
Affine transformation => 仿射 变化
In geometry, an affine transformation, affine map or an affinity (from the Latin, affinis, “connected with”) is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines 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.
Examples of affine transformations include translation, scaling, homothety, similarity transformation, reflection, rotation, shear mapping, and compositions of them in any combination and sequence.