Surface Representation of Particle Based Fluids

In this thesis, we focus on surface representations for particle-based fluid simulators such as Smoothed Particle Hydrodynamics (SPH). We first present a new surface reconstruction algorithm that formulates the implicit function as a sum of anisotropic smoothing kernels. The direction of anisotropy at a particle is determined by performing Weighted Principal Component Analysis (WPCA) over the neighboring particles. In addition, we perform a smoothing step that re-positions the centers of these smoothing kernels. Since these anisotropic smoothing kernels capture the local particle distributions more accurately, our method has advantages over existing methods in representing smooth surfaces, thin streams and sharp features of fluids. This method is fast, easy to implement, and the results demonstrate a significant improvement in the quality of reconstructed surfaces as compared to existing methods. Next, we introduce the idea of using an explicit triangle mesh to track the air/liquid interface in a SPH simulator. Once an initial surface mesh is created, this mesh is carried forward in time using nearby particle velocities to advect the mesh vertices. The mesh connectivity remains mostly unchanged across time-steps; it is only modified locally for topology change events or for the improvement of triangle quality. In order to ensure that the surface mesh does not diverge from the underlying particle simulation, we periodically project the mesh surface onto an implicit surface defined by the physics simulation. The mesh surface presents several advantages over previous SPH surface tracking techniques: Our method for surface tension calculations clearly outperforms the state of the art in SPH surface tension for computer graphics. Our method for tracking detailed surface information (like colors) is less susceptible to numerical diffusion than competing techniques. Finally, a temporally-coherent surface mesh allows us to simulate high-resolution surface wave dynamics without being limited by the particle resolution of the SPH simulation.