Long range constraints for rigid body simulations

The two main constraints used in rigid body simulations are contacts and joints. Both constrain the motion of a small number of bodies in close proximity. However, it is often the case that a series of constraints restrict the motion of objects over longer distances such as the contacts in a large pile or the joints in a chain of rigid bodies. When only short range constraints are considered, a large number of solver iterations is typically needed for long range effects to emerge because information has to be propagated through individual joints and contacts. Our basic idea to significantly speed up this process is to analyze the contact or joint graphs and automatically derive long range constraints such as upper and lower distance bounds between bodies that can potentially be far apart both spatially and topologically. The long range constraints are either generated or updated at every time step in case of contacts or whenever their topology changes within a joint graph. The significant increase of the convergence rate due to the use of long range constraints allows us to simulate scenarios that cannot be handled by traditional solvers with a number of solver iterations that allow real time simulation.