Ignoring the effects that gravity and other external forces may haveon tissue, some researchers have concentrated on the deformationsthat occur in the vicinity of joints. One simplifying assumption considersthe human body as consisting of rigid body parts connectedwith flexible surfaces at joints. Chadwick et al. use free-formdeformations to deform skin surfaces that surroundthe underlying skeleton. By using abstract muscle operators, a relationshipbetween skeletal parameters (such as joint angles) andthe control points of the FFDs is established. For example, tendonmuscle operators are used to control deformations near joints.The Thalmanns use joint-dependent local deformation operatorsto control the changes that surfaces undergo near flexing joints.Singh models the skin surfaces near joints with polyhedral objectsembedded in implicit functions. As the joints move, the implicitfunctions deform the polyhedral definition, and therefore theskin surface in the vicinity of the joint.Surfaces may also be deformed in areas other than near joints.Chadwick et al. use flexor muscle operators based on FFDsto simulate the visible result of muscle contraction, while Nahaset al. manipulate the control points of a B-spline model tomimic deformations. Henne [10] and Singh both use implicitfunction primitives to model muscles and pseudo-physical modelsto cause these muscles to bulge. None of these methods model individualmuscles in an anatomically appropriate way, nor do any ofthem attempt to account for all muscles that create or influence thevisible surfaces surrounding the underlying skeleton.Early physically-based techniques for modeling facial expressionsconsider the face to be sufficiently representable by its skin,applying abstract muscle actions to the skin to produce facial expressions. The work of Waters in this regard is particularlynoteworthy. More recent physically-based techniques areanatomically more appropriate . Pieper [16] developed a modelof soft tissue which accounts for the 3D structure and mechanicalproperties of human facial tissue, allowing accurate simulation ofthe interaction between soft tissue, muscles, and bony structures inthe face. Waters extended his earlier work by using a physicalmodel of the epidermis, subcutaneous fatty tissues, and bone tomodel facial expressions more realistically.Chen and Zeltzer developed a finite element model of muscleto simulate muscle forces and to visualize the deformations thatmuscles undergo during contraction. They used polygonal data derivedfrom MRI scans or data digitized from anatomically accurateplastic models to represent muscles. Their model accounts forshape changes due to external forces, such as gravity, or due to internalmuscle forces which produce movement.In her approach to modeling and animating animals, Wilhelmsuses ellipsoids tomodel bones, muscles, and fatty tissue.She uses an iso-surface extraction program to generate polygonalskin surfaces around the ellipsoids in some rest posture of the body,and anchors the skin to the underlying body components, allowingthe skin to be adjusted automatically when the body moves. Herresearch concentrates on the generation of models that may be developedat least semi-automatically.
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