A Muscle Model for Animating Three-Dimensional Facial Expressions by Keith Waters SIGGRAPH proceedings 1987Existing approaches to facial animation (in 1987) - Key framing – requires complete specification of the model at each extreme, data-intensive - Parameterization – requires that the topological mesh of the face stays the same, may not work for different face types.Facial Action Coding System (FACS) Notational-based environment for deriving emotional states from facial distortion (developed by Paul Ekman and Wallice Friesden) Individual muscles (or groups of muscles) are defined as Action Units that distort the skin.FACS Action Unit AU1activation produces expression of fearComputer model for muscles of the face  Two major muscle groups:  Lateral/parallel muscles that pull  Sphincter muscles that squeeze  Parameters in facial modeling  Muscle strength (spring constant)  Skin elasticity  Proximity of the node on the face surface to the muscle  The size of the displacementMuscles as vectors  Directed towards the point of attachment to the bone  Magnitude is zero at the bony attachment, increases towards point of insertion into the skin (no displacement at the bony attachment  Concave zone of influence Muscle vector displacing 3d gridMuscle vector model x’ = f(K,A,R,x) y’ = f(K,A,R,y) K - muscle spring constant Ω - maximum zone of influence D – vector V1P distance A – angular displacement R – radial displacement A = cos(µ/π . π/2) R = cos((1-D/Rs) π/2) (for points inside V1 Pn Pm) R = cos((D-Rs)/(Rf-Rs) π/2) (for points inside Pn Pr Ps Pm Rs – fallstart of muscle pull Rf – fall finish of muscle pull3D Muscle Vector Zone of influence = 35 fallstart = 7.0, fallfin = 14.0 muscle spring constant = 0.75 elastisity = 1.0 and 10.03D Vector for sphincter muscle x’ = f(K,R,x) y’ = f(K,R,y) No angular displacement for the sphincter muscles.Confluence of two muscle vectors For each node a degree of freedom (maximum displacement) has to be determined. Each node stores the information about its attractors.Model creation – data structure Face modeled with a polygonal data structureModel creation - implementation Program driven by those parameters: For linear muscles:  Zone of influence  Fallstart  Fallfin  Muscle spring constant  Elasticity For sphincter muscles:  Tension  Horizontal and vertical axisRendering Relaxed HappyRendering Fear