APPLYING CONSTRAINED OPTIMIZATION TO COMPUTER-GRAPHICS

For many years, objects in computer-generated animation moved only as an animator moved them. In the last few years, physically-based modeli ng techniques have demonstrated that more attractive and realistic-see ming motion can be created by subjecting objects to forces and constra ints and making the objects move as they would in a physical environme nt. Sometimes the environment is under- or over-constrained. In these cases, numerical optimization is used to find the best movement path t he objects, where ''best'' is evaluated according to user-specified cr iteria. This article discusses some of the previous results using this technique, identifies some future uses, including some that are likel y to become commonplace in a few years, and describes numerical method s to solve these problems.