Explicitly Symplectic Algorithm for Long-time
Simulation of Ultra-flexible Cloth
Xiao-hui
Tan1, Zhou Mingquan2, Yachun Fan2, Wang
Xuesong2, and Wu Zhongke2
1College of Information and Engineering,
Capital Normal University, China
2College of Information Science and
Technology, Beijing Normal University, China
Abstract: In
this paper, a symplectic structure-preserved algorithm is presented to solve
Hamiltonian dynamic model of ultra-flexible 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
platform-World Max Studio.
Keywords: Flexible cloth simulation, numerical
integration, symplectic method, scene building system.