Abstract: A hierarchical 3D graphics model can be viewed as a hierarchical graph of its nodes and their associated motions, with the mathematical type of motions graphically indicated. A user can click on a displayed motion to edit it. A motion API provides one or more of the following features: (1) spatial predicate functions; (2) functions for scaling motion intensity; (3) classes for shake, spin, and swing motions; (4) motion classes with a GUI interfaced for defining their duty cycle; (5) functions for defining and computing 0th through 2nd order derivatives of 3D position and orientation as function of time; (6) behaviors that constrain motions by boundaries in which the constraint is a reflection, clamp, andor onto constraint, or in which the boundary is a composite boundary. Motions can be defined by successive calls to an API and then be saved in a file.