Basic 2D transformations

An object in 3D space can cast a projection in 2D space that is different from the original projection. Such transformations are called 2D transformations. They are shown in the following image. We will use some of these transformations to explain concepts discussed later in the chapter and also in other chapters:

We write these transformations in the mathematical form, along with their matrix representations, as shown here:

• Translation: The mathematical representation of a translation transformation is given by:

  

• Affine: The mathematical representation of an affine transformation is given by:

  

• Rigid: The mathematical representation of a rigid transformation is given by:

  

• Projective: The mathematical representation of a projective transformation is given by: