Physics-based animation tools for fluids and surfaces: Generating surfaces from fluids, animating fluids on surfaces and controlling fluids from surfaces

In this dissertation, I will address three problems in the area of physics-based animation related to surfaces---extraction of smooth, temporally coherent surfaces from animated particle data-sets; fluid simulation on unstructured quadrilateral surface meshes; and interpolation of velocity fields that preserve rotations for fluid control methods.;The first problem is to generate surfaces from animated particle data---particle skinning. I cast the problem in terms of constrained optimization and solve the optimization using a level-set approach. The optimization seeks to minimize the thin-plate energy of the surface, while staying between surfaces defined by the union of spheres centered at the particles. My approach skins each frame independently while preserving the temporal coherence of the underlying particle animation. Thus, it is well-suited to environments where particle skinning is treated as a postprocess, with each frame generated in parallel. Moreover, my approach is integrated with the OpenVDB library and the underlying partial differential equation is amenable to implicit time integration. I demonstrate our method on data generated by a variety of fluid simulation techniques.;I present a method for fluid simulation on unstructured quadrilateral surface meshes. I solve the Navier-Stokes equations by performing the traditional steps of fluid simulation, semi-Lagrangian advection and pressure projection, directly on the surface. I include level-set-based front-tracking for visualizing ''liquids,'' while we use densities to visualize "smoke.'' I demonstrate our method on a variety of meshes and create an assortment of visual effects.;Fluid control methods often require the interpolation of surface velocities throughout the interior of a shape to use the surface velocity as a feedback force or as a boundary condition. Prior methods for interpolation in computer graphics, namely velocity extrapolation in the normal direction and potential flow, suffer from a common problem; they fail to capture the rotational components of the velocity field, although extrapolation in the normal direction does consider the tangential component. I address this problem by casting the interpolation as a steady state Stokes flow. This type of flow captures the rotational components and is suitable for controlling liquid animations where tangential motion is pronounced, such as in a breaking wave.