Killer Game Programming in Java

Forward and Inverse Kinematics

Before talking about forward and inverse kinematics, it's useful to review the parent-child relationship utilized by the nodes in a Java 3D scene graph. This hierarchy is particularly important for sequences of TransformGroup nodes.

Figure 20-6 shows a simple hierarchy made up of a parent and a child TransformGroup. The parent holds a translation of (1, 1, 2), and the child a translation of (2, 3, 1). However, from the world's viewpoint, the child's translation will be (3, 4, 3), a combination of the parent and child values. Here, the combination is an addition of the local translations, but it becomes more complicated when introducing rotation and scaling elements.

Figure 20-6. A hierarchy of TransformGroups

In general, the world (or scene) view of a TransformGroup is a combination of its translation, rotations, and scaling with those of its ancestors (parent, grandparent, and so on).

This hierarchy is important when developing an articulated figure since each limb contains several TransformGroups, and the connection of limbs to make the complete figure creates a large hierarchy of TransformGroups. The consequence is that when a limb is moved (by affecting one of its TransformGroups), the limbs linked to it as children will also move.

This top-down behavior is at the heart of forward kinematics, one of the standard approaches to animating articulated figures. ...