Explicitly Symplectic Algorithm for Long-time Simulation of Ultra-flexible Cloth

In this paper, a symplectic structure-preserved algorithm is presented to solve Hamiltonian dynamic model of ultraflexible cloth simulation with high computation stability. Our method can preserve the conserved quantity of a Hamiltonian, which enables a long-time stable simulation of ultra-flexible cloth. Firstly, the dynamic equation of ultra-flexible cloth simulation is transferred into Hamiltonian system which is slightly perturbed from the original one, but with generalized structure preservability. Secondly, semi-implicit symplecticRunge-Kutta and Euler algorithms are constructed, and able to be converted into explicit algorithms for the separable dynamic models. Thirdly, in order to show the advantages, the presented algorithms are utilized to solve a conservative system which is the primary ultra-flexible cloth model unit. The results show that the presented algorithms can preserve the system energy constant and can give the exact results even at large time-step, however the ordinary non-symplectic explicit methodsexhabit large error with the increasing of time-step. Finally, the presented algorithms are adopted to simulate a large-areaultra-flexible cloth to validate the computation capability and stability. The method employs the symplectial features and analytically integrates the force for better stability and accuracy while keeping the integration scheme is still explicit. Experiment results show that our symplectic schemes are more powerful for integrating Hamiltonian systems than non-symplectic methods. Our method is a common scheme for physically based system to simultaneously maintain real-time and long-time simulation.It has been implemented in the scene building platformWorld Max Studio.