Interactive cutting of finite elements based deformable objects in virtual environments

There is a wide range of virtual reality (VR) applications that benefit from physically based modeling, such as assembly simulation, robotics, training and teaching (e.g., medical, military, sports) and entertainment. The dynamics of rigid bodies is well understood and several open source as well as commercial physics engines supporting articulated rigid bodies and particle systems are available. On the other hand, the simulation of deformable bodies is an objective of current research. The main application areas of deformable objects simulation in computer graphics and VR are the simulation of cloth and medical simulation. The challenge of VR applications is the real time simulation requirement. The raising computational power of the last decades allowed for adapting selected methods known from engineering sciences for interactive simulation. The simulation of cutting is especially challenging though, as most methods suffer from both performance and stability issues. Although a number of approaches have been presented over the last decade, the problem has not been solved satisfyingly, yet. This thesis presents methods for an interactive simulation of finite elements based deformable objects as used, e.g., in VR surgical simulators. The main objectives of such simulators are stability and performance of the employed methods allowing for an interactive object manipulation including topological changes in real time. A novel method for interactive cutting of deformable objects in virtual environments is presented. The key to this method is the usage of the extended finite elements method (XFEM). The XFEM can effectively model discontinuities within an FEM mesh without creating new mesh elements and thus minimizing the impact on the performance of the simulation. The XFEM can be applied to advanced constitutive models used for the interactive simulation of large deformations. Moreover, an analysis of mass lumping techniques, showing that the stability of the simulation is guaranteed even when small portions of the material are cut is presented. The XFEM based cutting surpasses the currently most widely used remeshing methods in both, performance and stability and is suitable for interactive VR simulation. Further, a software architecture for physical simulation of deformable objects in VR applications is proposed. The framework is suitable for the creation of complex VR applications as, e.g., a virtual surgical trainer. It uses thread level task parallelization for the concurrent execution of visualization, collision detection, haptics and deformation. Moreover, a parallelization approach for the deformation algorithm, which is the most computationally intensive part is proposed. The presented solution based on OpenMP requires only minimal changes to the source code while achieving a speedup comparable to the results of more sophisticated approaches. The presented framework benefits from the current developments in the computing industry and allows an optimal utilization of multicore CPUs.