In our SIGGRAPH'2000 paper, we apply our work on geometric modeling to computer animation. Our goal is to embed free-form constraints into a graphical model. With such constraints a graphic can maintain its visual integrity-and break rules tastefully-while being manipulated by a casual user. A typical parameterized graphic does not meet these needs because its configuration space contains nonsense images in much higher proportion than desirable images, and the casual user is apt to ruin the graphic on any attempt to modify or animate it.
We therefore model the small subset of a given graphic's configuration space that maps to desirable images. In our solution, the basic building block is a simplicial complex-the most practical data structure able to accommodate the variety of topologies that can arise. The configuration-space model can be built from a cross product of such complexes. We describe how to define the mapping from this space to the image space. We show how to invert that mapping, allowing the user to manipulate the image without understanding the structure of the configuration-space model. We also show how to extend the mapping when the original parameterization contains hierarchy, coordinate transformations, and other nonlinearities.