Simulation and control of physical phenomena in computer graphics

In computer graphics applications such as feature animation and games there is a need to produce convincing simulations of phenomena such as smoke, water, cloth and rigid bodies. Computational physics is the natural framework for such simulations. The physical equations describing most of these phenomena are well known and have been extensively studied over the last couple of centuries by the physics community. Which solution technique to use in practice depends on the application. In computer graphics it is desirable to have fast and stable simulations. Ideally, the simulations should run in realtime. This is important of course in games but also in movie production houses where animators have to fine tune the parameters of the simulation. On the other hand it is also desirable that these simulations are easy to implement. This makes the code easier to maintain in a commercial system. Our experience has been that good solutions very often result in simple algorithms which are relatively easy to code. This paper mainly focuses on the simulation of fluids such as smoke, water and fire. Our fluid solver which was first introduced in Stam (1999) relies on a spatial discretization of space into voxels. The physical quantities describing the fluid such as velocity and density are assumed to be constant in each voxel. These values are updated over each time step to create an animation of a fluid flow.