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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 (1992) to provide explicit graduated control of the response of a deformable object to imposed forces. >

This paper presents Langwidere, a facial animation system that integrates hierarchical spline modeling with simulated muscles based upon local area surface deformations. The multi-level shape representation of a hierarchical spline provides control over the extent of deformations, while at the same time reducing the amount of data needed to define the surface. The facial model is constructed from a single closed surface defining the entire head and internal structures of the mouth cavity. Simulated muscles are attached to various levels of the surface with more rudimentary levels substituting for bone such as the skull and jaw. The combination of a hierarchical model and simulated muscles provides a smooth surface with precise and flexible control over surface shape. >