REALISTIC ANIMATION OF LIQUIDS

We present a comprehensive methodology for realistically animating liq uid phenomena. Our approach unifies existing computer graphics techniq ues for simulating fluids and extends them by incorporating more compl ex behavior. It is based on the Navier-Stokes equations which couple m omentum and mass conservation to completely describe fluid motion. Our starting point is an environment containing an arbitrary distribution of fluid, and submerged or semisubmerged obstacles. Velocity and pres sure are defined everywhere within this environment and updated using a set of finite difference expressions. The resulting vector and scala r fields are used to drive a height field equation representing the li quid surface. The nature of the coupling between obstacles in the envi ronment and free variables allows for the simulation of a wide range o f effects that were not possible with previous computer graphics fluid models. Wave effects such as reflection, refraction, and diffraction, as well as rotational effects such as eddies, vorticity, and splashin g are a natural consequence of solving the system. In addition, the La grange equations of motion are used to place buoyant dynamic objects i nto a scene and track the position of spray and foam during the animat ion process. Typical disadvantages to dynamic simulations such as poor scalability and lack of control are addressed by assuming that statio nary obstacles align with grid cells during the finite difference disc retization, and by appending terms to the Navier-Stokes equations to i nclude forcing functions. Free surfaces in our system are represented as either a collection of massless particles in 2D, or a height field which is suitable for many of the water rendering algorithms presented by researchers in recent years. (C) 1996 Academic Press, Inc.