Effiziente Animation virtueller Bekleidung

One aim in simulating cloth is to reproduce the motion of cloth as realistic as possible with minimal effort. In physically based modeling the state of cloth is numerically changed by integrating the equation of motion. Because of the high stiffness of the underlying differential equation implicit integration methods prove to be superior to explicit integration methods. The most expensive step in (semi-)implicit integration is about solving a linear system. In most simulation systems this solution is computed by the relative efficient conjugate gradients algorithm. The core of this work is the introduction of multigrid methods into the area of textile simulation that lower the computational costs of solving precisely this linear system. The faster convergence is obtained by heavily reducing the number of expensive cg-iterations on the finest grid. Therefore multigrid methods include calculations on many grids of different discretication levels inside the solution process. After a general introduction to multigrid methods efficient algorithms for the work with multiple grids in the area of textile simulation are presented. This includes the construction of coarse grids and corresponding operators to change between these as well as the embedding into a complex simulation system. The decrease of computational costs is proven by comparing performance of the standard cg-method and the newly invented multigrid method. The experiments were done based on a rectangular discretized model of cloth connected by cubic springs that is embedded in an environment with gravity and airdrag. By using a cubic spring model instead of the commonly used linear spring model the highly nonlinear load-deflection behaviour of cloth could be better approximated and more stable and visually more pleasant simulations according to that model could be observed