Rigid Body Cable for Virtual Environments

The present paper addresses the real-time simulation of cables for virtual environments. A faithful physical model based on constrained rigid bodies is introduced and discretized. The performance and stability of the numerical method are analyzed in detail and found to meet the requirements of interactive heavy hoisting simulations. The physical model is well behaved in the limit of infinite stiffness, as well as in the elastic regime, and the tuning parameters correspond directly to conventional material constants. The integration scheme mixes the well-known Stormer-Verlet method for the dynamics equations with the linearly implicit Euler method for the constraint equations and enables physical constraint relaxation and stabilization terms. The technique is shown to have superior numerical stability properties in comparison with either chain-link systems or spring and damper models. Experimental results are presented to show that the method results in stable real-time simulations. Stability persists for moderately large fixed integration step of Deltat = 1/60 s, with hoisting loads of up to 105 times heavier than the elements of the cable. Further numerical experiments validating the physical model are also presented.