Controlling Rigid Bodies with Dynamic Constraints

Abstract

We present a technique, "Dynamic Constraints," for controlling the positions and orientations of rigid bodies n computer graphics models. The technique addresses the issue of providing control over a physically-based model, in which the bodies' behavior is determined by simulation of Newton's Laws of Motion. The "Dynamic Constraints" technique allows the modeler to control the configuration of bodies in a model by specifying constraints which must be met and maintained, as the simulation unfolds. To meet the constraints, we introduce forces into the model; these "constraint forces" forces are applied to the bodies that are constrained. We use an inverse dynamics method to derive a linear "constraint-force equation," whose solution yields the values of the constraint forces. We continually solve the constraint-force equation during the simulation of a model, so that the bodies' behavior will be consistent with the constraints. This thesis is accompanied by a narrated 10 -minuted videotape, "Caltech Modeling Demos, 1987" that contains several animations demonstrating the "Dynamic Constraints" technique. This thesis additionally includes a glossary of terms relating to physically-based modeling and dynamic constraints.