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 modeling techniques have demonstrated that more attractive and realistic-seeming motion can be created by subjecting objects to forces and constraints and making the objects move as they would in a physical environment. Sometimes the environment is under- or over-constrained. In these cases, numerical optimization is used to find the best movement path the objects, where “best” is evaluated according to user-specified criteria. This article discusses some of the previous results using this technique, identifies some future uses, including some that are likely to become commonplace in a few years, and describes numerical methods to solve these problems