A Modified Numerical Integration Method for Deformable Object Animation

Abstract

A satisfied deformable object simulation should be general, accurate, efficient and stable. Explicit, implicit and semi-implicit numerical integration methods have contributed to large performance enhancements in the field of deformable simulation. Cloth is the most representative deformable object. In this paper, we propose an improved embedded Runge-Kutta integration method to solve the deformable simulation that based on classical spring-mass model. Traditional embedded Runge-Kutta methods generally solve ordinary differential equations of deformable object simulation. Most of them tend to concentrate on the efficiency of the simulation process, and not the fidelity of the simulation result. We investigate and determine the extent to which the overall quality must be compromised in order for the stable conditions to be satisfied. The improved Runge-Kutta method proposed in our paper incorporates the fixed time step and adaptive time step in solving cloth motion equations to achieve a controllable error evaluation. Compared with the other Runge-Kutta methods, the proposed method has some advantages for cloth simulation: controllable error evaluation without extra computations, excellent efficiency, good stability and satisfied precision. Experiment demonstrates that this method results in simulation efficiency improvements and is considerable practicable. © Springer-Verlag Berlin Heidelberg 2007.