Geometric transformation


In mathematics, a geometric transformation is any bijection of a set to itself with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is injective so that its inverse exists. The study of geometry may be approached via the study of these transformations.
Geometric transformations can be classified by the dimension of their operand sets. They can also be classified according to the properties they preserve:
Each of these classes contains the previous one.
Transformations of the same type form groups that may be sub-groups of other transformation groups.