Controlling fluid animation with geometric potential

We propose a new fluid control technique that uses a geometrically induced potential field. Instead of optimizing the control forces exerted at each frame, as was done in previous work, a potential is added as an extra dimension to the simulation space which coerces the fluid inside this space to form the target shape. This type of shape control requires practically no additional computing by the Navier-Stokes solver at run-time, and adds little overhead to implementation. The confinement potentials are induced from geometric information given by animators, and so the control forces that take fluids to a lower potential can be decided in a preprocessing step. We show that a slightly generalized Navier-Stokes equation for fluids in potential fields can be simulated without changing the solver itself. A harmonic potential function can be quickly found with the Poisson solver which is already implemented as a part of the Navier-Stokes solver. 2 and 3 dimensional flows designed by common methods such as hand drawing, traditional shape modeling and key-framing, can be animated efficiently with our control technique. Copyright (C) 2004 John Wiley Sons, Ltd.