Mastering Affine Transformations

Throughout the book so far, you’ll have gained an appreciation for the variety of methods used to move, rotate, and scale vectors and points. To move a mesh from one location in space to another requires each vertex in that mesh to be moved, and then the mesh is redrawn. This movement (formally called a translation) is just one of a set of special point and vector manipulator methods called affine transformations.

Affine transformations are important in computer graphics primarily, as they allow for the manipulation of a set of vertices without losing the integrity of the form. By this, I mean that any lines and planes in a mesh retain their relative parallelism and ratios. This might sound a little abstract, so let’s illustrate it with an example. Consider the diagram in Figure 12.1:

Figure 12.1: An affine transformation of a cube

Figure 12.1 shows an original cube in (a) made up of six sides and eight vertices...