Facial Animation - Computer Animation: Algorithms and Techniques - page 329

skin

muscle layer

bone

muscle
point of attachment point of insertion

FIGURE 10.15
Cross section of the tri-layer muscle as presented by Parke andWaters [ 27 ] ; the muscle only directly affects nodes
in the muscle layer.

I

(a)

d 0 = d

d

A

I

k
R

(b) cos 1.0

￿

0 k R

d

d k = d

￿

2.0

k

otherwise

= 0

B

(c)

k
R

f

cos 1.0 sin 1.0

￿

￿

0 f

d k f = d

￿ ￿

I 2.0

2.0

k

otherwise

= 0

d

FIGURE 10.16
Sample attenuation: (a) insertion point I is moved d by muscle; (b) point A is moved d k based on linear distance

from the insertion point; and (c) point B is moved d k f based on the linear distance and the deviation from the

insertion point displacement vector.

by the muscle. How the deformation propagates along the skin as a result of that muscle determines
how rubbery or how plastic the surface will appear. The simplest model to use is based on geometric
distance from the point and deviation from the muscle vector. For example, the effect of the muscle
may attenuate based on the distance a given point is from the point of insertion and on the angle of
deviation from the displacement vector of the insertion point. See Figure 10.16 for sample calculations.
A slightly more sophisticated skin model might model each edge of the skin geometry as a spring and
control the propagation of the deformation based on spring constants. The insertion point is moved by
the action of the muscle, and this displacement creates restoring forces in the springs attached to the
insertion point, which moves the adjacent vertices, which in turn moves the vertices attached to them,
and so on (see Figure 10.17 ) . The more complicated Voight model treats the skin as a viscoelastic