Facial Animation - Computer Animation: Algorithms and Techniques - page 330

Applied
Force

vertex
connected by
5 springs to vertex
force is applied to

FIGURE 10.17
Spring mesh as skin model; the displacement of the insertion point propagates through the mesh according to the
forces imparted by the springs.

Damper

Spring

d i n i ￿ d
dt

V i 1 V i 2 V i 1 V i 2

F i = k i ￿

FIGURE 10.18
Voight viscoelastic model; the motion induced by the spring forces is damped. Variables

k and n are spring and

damper constants, respectively; and d i is the rest length for the spring.

element by combining a spring and a damper in parallel ( Figure 10.18 ). The movement induced by the
spring is damped as a function of the change in length of the edge.
The muscle model determines the function used to compute the contraction of the muscle. The alter-
natives for the muscle model are similar to those for the skin, with the distinction that the muscles are
active elements, whereas the skin is composed of passive elements. Using a linear muscle as an exam-
ple, the displacement of the insertion point is produced as a result of muscle activation. Simple models
for the muscle will simply specify a displacement of the insertion point based on activation amount.
Because, in the case of the orbicularis oris, muscles are attached to other muscles, care must be taken in
determining the skin displacement when both muscles are activated.
More physically accurate muscle models will compute the effect of muscular forces. The simplest
dynamic model uses a spring to represent the muscle. Activating the muscle results in a change of its
rest length so as to induce a force at the point of insertion. More sophisticated muscle models include
damping effects. A muscle model developed by clinical observation is shown in Figure 10.19 . How-
ever, spring-based facial muscles often result in a computationally expensive approach, and jiggling of
the skin can be difficult to control.