Modeling time and topology for animation and visualization with examples on parametric geometry

The art of animation relies upon modeling objects that change over time. A sequence of static images is displayed to produce an illusion of motion. Even for simple cases, a careful analysis exposes that formal topological guarantees are often lacking. This absence of rigor can result in subtle, but significant, topological flaws. A new modeling approach is proposed to integrate topological rigor with a continuous model of time. Examples will be given for Bézier curves, while indicating extensions to a richer class of parametric curves and surfaces. Applications to scientific visualization for molecular modeling are discussed. Prototype animations are available for viewing over the web.