A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions

Simulating multi-object collisions in real-time environments remains a significant challenge, particularly when handling simultaneous collisions in a physically accurate manner. Traditional Gauss-Seidel solvers, widely employed in physics engines, often fail to preserve the symmetry and consistency of multi-object interactions that are often observed in physics. In this paper, we present a generalized and robust Gauss-Seidel solver to overcome the difficulties in simultaneous collisions. Using spatial and temporal collision states to classify and resolve constraints, our algorithm ensures correct collision propagation and symmetry, addressing the limitations commonly found in existing solvers. Moreover, our algorithm can mitigate jitters caused by floating-point errors, ensuring smooth and stable collision responses. Our approach demonstrates fast convergence and improved accuracy in scenarios involving complex multi-object collisions.