A Multilevel Approach to Surface Response in Dynamically Deformable Models

Discretized representations of deformable objects, based upon simple dynamic point-mass systems, rely upon the propagation of forces between neighbouring elements to produce a global change in the shape of the surface. Attempting to make such a surface rigid produces stiff equations that are costly to evaluate with any numerical stability. This paper introduces a new multilevel approach for controlling the response of a deformable object to external forces. The user specifies the amount of flexibility or stiffness of the surface by controlling how the applied forces propagate through the levels of a multi-resolution representation of the object. A wide range of surface behaviour is possible, and rigid motion is attained without resort to special numerical methods. This technique is applied to the displacement constraints method of Gascuel and Gascuel to provide explicit graduated control of the response of a deformable object to imposed forces.