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Time Reversal and Simulation Merging for Target-Driven Fluid Animation

We present an approach to control the animation of liquids. The user influences the simulation by providing a target surface which will be matched by a portion of the liquid at a specific frame of the animation; our approach is also effective for multiple target surfaces forming an animated sequence. A source simulation provides the context liquid animation with which we integrate the controlled target elements. From each target frame, we compute a target simulation in two parts, one forward and one backward, which are then joined together. The particles for the two simulations are initially placed on the target shape, with velocities sampled from the source simulation. The backward particles use velocities in the opposite direction as the forward simulation, so that the two halves join seamlessly. When there are multiple target frames, each target frame simulation is computed independently, and the particles from these multiple target simulations are later combined. In turn, the target simulation is joined to the source simulation. Appropriate steps are taken to select which particles to keep when joining the forward, backward, and source simulations. This results in an approach where only a small fraction of the computation time is devoted to the target simulation, allowing faster computation times as well as good turnaround times when designing the full animation. Source and target simulations are computed using an off-the-shelf Lagrangian simulator, making it easy to integrate our approach with many existing animation pipelines. We present test scenarios demonstrating the effectiveness of the approach in achieving a well-formed target shape, while still depicting a convincing liquid look and feel.