| Generating natural phenomena in a virtual world has a number of practical applications. Thanks to the rich and complicated details in the real world, the goal of realistically and efficiently reproducing natural phenomena in a digital world is well known as an open problem for graphics researchers.;In this dissertation, three different issues in modeling liquid animations have been addressed. First, a virtual surface method and its 3D numerical solution is proposed to account for surface tension effects and their interactions with solid surfaces in physically based fluid simulation. This allows us to generate various surface tension behaviors in small scale liquid, such as water drops, bubbles, water streamlets and capillary action.;The second issue that is addressed is how to make small scale fluid simulation more efficient. The solution proposed in this dissertation is a general shallow wave equation model, extended from the original shallow wave equations. By simplifying 3D incompressible fluid dynamics into a 2D problem under the shallow wave assumption, small scale liquid can be stably and efficiently simulated over arbitrarily curved surfaces, using implicit numerical schemes.;The third contribution is a novel hybrid framework for animating liquid that combines image based reconstruction techniques with physically based fluid simulation. While image based reconstruction cannot correctly generate fluid animations alone frame by frame due to depth reconstruction noise and errors, physically based simulation is used as a refinement tool to enforce incompressible fluid dynamics over the initial reconstruction by propagating shape information back and forth in space and time. In this way, water animations can be realistically and faithfully generated from images without error accumulation or stability issues as in physically based simulation. The whole process is also more efficient than physically based simulation, because physics is only used to achieve temporal coherence rather than to generate the whole animation. |
