The machinery of linear algebra can be used to express many of the operations required to arrange objects in a 3D scene, view them with cameras, and get them onto the screen. Geometric transformations like rotation, translation, scaling, and projection can be accomplished with matrix multiplication, and the transformation matrices used to do this are the subject of this chapter.
We will show how a set of points transforms if the points are represented as offset vectors from the origin, and we will use the clock shown in Figure 6.1 as an example of a point set. So think of the clock as a bunch of points that are the ends of vectors whose tails are at the origin. We also discuss how these transforms operate differently ...