Two-Dimensional Transformations

Abstract

A 2D transformation is a function or a mapping, which when applied to a 2D point P = ⟨x, y⟩ will transform it (map it) onto another 2D point P′ = ⟨x′, y′). So a 2D transformation transforms a set of original points, O, into a set of transformed points, T.

In this chapter we will focus our attention on the type of transformation in which any point P _i = ⟨x _i , y _i ⟩ of set O can be transformed to one and only one point P′ _i = ⟨x′ _i , y′ _i ⟩ of set T. Also no two points of set O can be transformed into the same point of set T. Such a transformation is said to be a one to one mapping (see Fig. 5.1)