The present invention consists of an evaluation engine, which is a system for evaluating the state of an animation at a specific time where secondary animation may be derived from the state of the animation at another time. Unlike DAG-based systems where time is another variable, time is external to the evaluation engine so that it can easily evaluate alternate times and even entire simulations. It also comprises meshes which support instancing and edge weights, and which employ and extensible system of polygon types to support subdivision surface approximation using a set of bi-quadratic patches which solve quickly. The meshes can also be animated by the evaluation engine using a mesh stack, which has multiple evaluation paths for quickly computing mesh attributes without performing a full evaluation.