A spring force formulation for elastically deformable models

Continuous deformable models are generally represented using a grid of control points. The elastic properties are then modeled using the interactions between these points. The formulations based on elasticity theory express these interactions using stiffness matrices. These matrices store the elastic properties of the models and they should be evolved in time according to changing elastic properties of the models. However, forming the stiffness matrices at any step of an animation is very difficult and sometimes the differential equations that should be solved to produce animation become ill-conditioned. Instead of modeling the elasticities using stiffness matrices, the interactions between model points could be expressed in terms of external spring forces. In this paper, a spring force formulation for animating elastically deformable models is presented. In this formulation, elastic properties of the materials are represented as external spring forces as opposed to forming complicated stiffness matrices. © 1997 Elsevier Science Ltd.