Physics-Based Animation Models Using Fractional Calculus
- Author(s): Özgen, Oktar
- Advisor(s): Kallmann, Marcelo
- et al.
Physics-based computer animation is an area of Computer Graphics with important applications ranging from visual effects in movies and computer games to simulation-based modeling and design. This dissertation introduces the use of fractional calculus for achieving new physics-based models in the areas of cloth and fluid simulation. Three main contributions are proposed. First, an underwater cloth deformation approach is introduced based on a half-derivative damping model. The cloth is represented by a system of particles connected by elastic elements with fractional damping terms that are able to well represent the history forces that happen underwater. As a result, underwater behavior is achieved without simulating the volumetric fluid around the cloth. Second, a new viscosity model employing fractional terms is proposed to better represent the behavior of colliding flows in simulations of Newtonian fluids based on Smoothed Particle Hydrodynamics (SPH). The fractional terms are integrated into the SPH equations in order to better capture the history-based exchanges that happen in regions of colliding flows. Finally, a model is introduced for simulating shear thickening fluids, which are a special type of non-Newtonian fluids that have not been simulated before in computer animation. The proposed model combines SPH forces with dynamic elastic forces that are modeled with history-based fractional stiffness terms. The model can successfully simulate both the solid and liquid-like behavior of a shear thickening fluid as well as the history-based phase transitions between the solid and liquid phases. The achieved model is able to produce results that are very similar to real-life experiments. This dissertation illustrates the potential of fractional calculus for modeling physics-based behavior and several numerical and visual experiments are presented to demonstrate the advantages of the proposed models.