Timo Eberl

• Geometric algebra provides a unified mathematical framework that combines many branches of physics and has recently found applications in computer science. Previous studies have demonstrated efficient implementations in applications such as ray tracing and inverse kinematics. This thesis focuses on the practical implementation of real-time rigid body physics using the 4D rigid geometric algebra (RGA). RGA includes algebraic representations for primitive geometries, namely points, lines and planes, and has operations for performing rigid transformations on them. The research presents approaches for applying these concepts to existing algorithms in the field of rigid body simulation and evaluates their real-time capability through runtime performance benchmarks. Performance measurements have shown that the runtime performance of an RGA implementation is comparable to conventional methods. In two algorithms a respective increase in execution time of 13% and 16% has been identified. It is estimated that a reduction in runtime performance of up to 20% compared to conventional methods can be expected when using RGA.