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Animation of surfaces with applications to cloth modelling

The realism requirements of virtual scenes in computer graphics have been increasing permanently. Therefore, geometric models do no longer suffice in some application areas. Textile simulation is one of these applications in which the models must be described by their physical behaviour. In computer animation, particle systems are frequently employed in order to animate surfaces. In this thesis particle systems are advanced so that they model continuous materials and approximate models of continuum mechanics. With such particle systems materials like textiles can be simulated without the material properties depending on the discretization. The particle system model describes the dynamics system by ordinary differential equations, and the actual simulation consists of solving these equations in time. Animations require that the solution be computed fast. Suitable implicit methods guarantee stability but make the computation of one time step very expensive. Hence, methods that reduce the costs of such time steps significantly are presented. The treatment of collisions is another problem in animation, and it will be shown that collisions can be implemented by a constraint mechanism. The collision response takes place stably and fast. Also resting contacts can be modelled. Furthermore, a method that refines the discretization adaptively in regions in which collisions occur is developed. This allows to achieve realistic results even with very coarse resolutions. The concepts developed in this work have been implemented in a system for cloth modelling. At the end of this work the software architecture of this implementation is described, and results are presented.