A
geometric transformation is any
bijection of a
set having some geometric structure to itself or another such set. Specifically, "A geometric transformation is a function whose domain and range are sets of points. Most often the domain and range of a geometric transformation are both R
2 or both R
3. Often geometric transformations are required to be 1-1 functions, so that they have inverses." The study of
geometry may be approached via the study of these transformations.