Efficient and Effective Algorithms for Controllable Fluid Simulation and Mesh Deformation

During the past decade, due to rapidly growing computational power, complicated numerical algorithms have become popular in graphics community which greatly improved the quality of graphics imagery. On the other hand, to produce high-quality visual effects, the size of the data being processed has also increased drastically at the same time. Thus efficient algorithms are desired in many applications. This dissertation focuses on problems in controlling fluid simulations and mesh deformations. It has potential applications in film and game industries. The first part of this dissertation includes efficient algorithms for controlling the motion of gas and liquid. The efficiency is achieved by using feedback forces to drive the fluid toward the target. Without expensive optimization procedures, the control algorithms produce desired and natural results that only incur an additional computational cost linear to the size of the problem. Controlling the motion of lightweight natural objects in a gaseous medium is also studied, using data-driven synthesis based on stylistic motion planning and nonlinear optimization based on smoothed particle hydrodynamics. In addition, we also introduce a simple algorithm to perform plausible fluid simulation over triangle meshes