Physics-Based Simulation

Summary

The Position Based Dynamics framework provides a robust and efficient method for physics-based simulation. Its core is a simple time-stepping loop that predicts new particle positions and then iteratively corrects them using a Gauss-Seidel solver. The mathematical basis for this correction is a projection derived from a linearized constraint function, weighted by inverse particle masses to produce physically plausible motion. This approach neatly sidesteps the stability problems of traditional explicit integrators. By defining different constraint functions, the same general solver can be used to simulate a wide variety of physical phenomena, from deformable solids to cloth and fluids. The framework is further enhanced by practical features like tunable stiffness and momentum-conserving damping, making it exceptionally well-suited for real-time applications.