The physical objects are constructed from conventional surface-based geometric models. The physical model is based on the action of a transformation on a set of mass particles embedded in the domain of the transformation. This set of mass particles is generated automatically from the geometric model. The transformations used for the physical model are the same as those commonly used in computer animation, including Free Form Deformations (FFD's). The physical model also includes shape restoration forces based on potential functions evaluated at discrete points throughout the domain of the transformation and drag forces based on the geometric model.
The models are animated through the use of constraints. Point constraints allow specific points on a model to be controlled kinematically. The trajectories of these points may be animated using standard key-frame animation techniques. Attachment constraints are used to attach a point on one model to a point on another. Attachment constraints are the equivalent to the construction of a motion hierarchy in a conventional animations system where the motion of one object is transferred to the motion of another object. Finally, plane constraints can be used to restrict the motion of a point on a model to a plane.
The Lagrangian form of the equations of motion is used to relate the acceleration of the parameters of the transformation to forces applied at points in the domain and forces generated by potential functions. In this setting the parameters of the transformation become the generalized coordinates of the dynamical system. The transformation parameters computed from the physical simulation are then applied to the geometric model to animate it. Since the transformations are the same as those used in conventional animation systems the physical simulation can be thought of as just another way of generating dynamic transformations in an animation system.
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