Discrete Physics-Based Models

The bodies of most fishes are highly deformable structures. We construct our dynamic fish model using a deformable mass-spring-damper system. There are several reasons for this choice:

• A mass-spring-damper model is a simple discrete mechanical structure capable of nonlinear, nonrigid dynamics.
• The spring-damper units in the model are viscoelastic units that serve both as geometric and deformation control primitives.
• Some viscoelastic units may be made actively contractile so that they serve as simple models of muscles.

Both passive and active deformable objects have been successfully animated using similar mass-spring-damper models. Terzopoulos et al. Terzopoulos87,Terzopoulos88 developed models for deformable objects capable of exhibiting a range of elastic behaviors. These models effectively animate the nonrigid motions of cloth, paper, metal, rubber, plastic, etc. The active contour models that we employed to compute texture mapping coordinates (see Chapter ) are also based on such models. Two instances of employing similar mass-spring models for animating active objects are the animation of snakes and worms [Miller1988] and the animation of human faces [Terzopoulos and Waters1990, Lee, Terzopoulos and Waters1995].

Xiaoyuan Tu

January 1996