Tracking and texturing liquid surfaces

This thesis addresses the problems of tracking and texturing liquid surfaces in computer graphics fluid simulations. The proposed surface tracking method, known as semi-Lagrangian contouring, takes the unusual approach of representing the liquid surface explicitly with a closed, manifold triangle mesh. However, rather than attempting to track the triangle mesh through time, a new triangle mesh is built at each timestep by contouring the zero-set of an advected signed-distance function. Thus, while we represent the surface explicitly, we update the surface through time using an implicit representation. One of the primary advantages of this formulation is that it enables tracking of surface characteristics, such as color or texture coordinates, at negligible additional cost. These advected surface characteristics can then be used in a variety of ways to generate time-coherent textures on the liquid surfaces. After considering a variety of simple texturing techniques, I propose an example-based texture synthesis method designed specifically for liquid animations. This example-based texture synthesis method first advects color values on the surface and then uses an optimization process to force the surface texture to more closely match a user-input example texture. This approach creates textures which resemble the example texture even in the precense of complicated topological changes and significant surface stretching/compression. I include a variety of examples demonstrating that these methods can be effectively used as part of a fluid simulation system to animate and texture complex and interesting liquid behaviors.