Pain and Agony using a Newton Based Method

The subject of this thesis is contact force determination, specifically for use in interactive rigid body simulation. The aim of the thesis is twofold, to overthrow the projected Gauss-Seidel method and replace it with a more accurate and robust method, and to propose a more accurate friction model than the one used in most interactive simulators. Part of the thesis is presented in the form of a paper [SNE09]. The paper was accepted for the 2009 workshop on Virtual Reality and Interactive Physical Simulation(VRIPHYS), held in Karlsruhe. Together with RAMBØLL A/S and NVIDIA, the image group at DIKU co-funded the travel expenses for four students, recognizing potential of the work presented in the four accepted papers. Although the method presented in [SNE09] has potential, it fails to be interactive for more than just small to medium sized simulations. For that reason, I have taken the first steps towards large scale interactive simulations, by posing a model based on proximal mappings. The proximal mapping model is independent of the friction model, making the friction model replaceable by any parameterization of a convex set. The implementation of this proximal mapping model remains to be done, but it shows potential.