The arm would end inside the body instead the shoulder

146 Chapter 3 Affine Transformations

W = TbodyRbodySbodyTarmRarmSarm

As we’ve indicated, the body and arm are treated as two separate objects, each with its own transformations, placed in a hierarchy. The body transformation is relative to world space, and the arm transformation is relative to the body’s space. When rendering, for example, we begin by drawing the body with its world transformation and then drawing the arm with the concatenation of the body’s transformation and the arm’s transformation. By doing this,

Figure 3.21b Mapping body and arm to world space.

we can change them independently — rotating the arm around the shoulder, for example, without affecting the body at all. Similar techniques can be used to create deeper hierarchies; for example, a turret that rotates on top of a tank chassis, with a gun barrel that elevates up and down relative to the turret.