Simulation and animation of deformable bodies

The generation and visualisation of moving virtual objects is of particular concern in computer graphics. Most notably, the animation of deforming models is complex depending on mechanical properties and the variability of the geometry. Purely geometric methods are, to some extend, sufficient to compute natural movements and deformations of a body. In other cases, a physics-based simulation is required. Both practices are applied to the animation of human characters, textiles, and soft bodies. Regarding character animation, we capture real movements from human actors and form a new virtual motion without losing important details of the movements. For this purpose, trajectories of individual prototypes are transformed on the basis of correspondences. Afterwards, an interpolation of the velocities produces a combination of the trajectories with the designated properties. The animation of the clothing is subject to physics-based methods. To realise an efficient simulation, we detect collisions early using dedicated bounding volume hierarchies. In this process, self-collisions are determined by analysing the local curvature of the surface. To compute soft body deformations, we particularly aim for an efficient implementation of elasticity theory by means of finite elements and consider stiff and nearly incompressible materials. To this end, we introduce finite tetrahedra with quadratic basis functions and perform an efficient numerical integration of the elastic forces. The bounding volume hierarchies are used again for the collision detection. Our simulation is applied to the interactive modelling of large meshes as well as the interaction with virtual tissue. Hence, the proposed methods are of interest not only for computer graphics in the narrow sense, but also for medical applications.