The use of forward difference equations in animation of physical phenomena

In the entertainment industry graphical images are often produced without adherence to physically accurate models. This is usually the case because there is a need to reduce production time and costs. The physical scientist, on the other hand, must produce graphical images that are accurate simulations of the physical phenomena they are attempting to visualize. Frequently the data that an accurate simulation produces can be difficult to use for rendering the animation. This paper describes the use of numerical methods to minimize the number of keyframes for an accurate animation.