Geometric transformation

In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning, such as preserving distances, angles, or ratios (scale). More specifically, it is a function whose domain and range are sets of points — most often both ${\displaystyle \mathbb {R} ^{2}}$ or both ${\displaystyle \mathbb {R} ^{3}}$ — such that the function is bijective so that its inverse exists.^[1] The study of geometry may be approached by the study of these transformations, such as in transformation geometry.^[2]