Constraint databases provide a very expressive framework for spatiotemporal database applications. However, animating such databases is difficult because of the cost of constructing a graphical representation of a single snapshot of a constraint database. We present a novel approach that makes the efficient animation of constraint databases possible. The approach is based on a new construct: parametric polygon. We present an algorithm to construct the set of parametric polygons that represent a given linear constraint database. We also show how to animate objects defined by parametric polygons, analyze the computational complexity of animation, and present empirical data to demonstrate the efficiency of our approach.≠