Research On Flexible Object Simulation Algorithm Based On Trapezium Formula

Flexible Object simulation systems are mainly based on geometrical, physical and hybrid techniques. Since adopting physical technique can not only embody the appearance but also analyze the internal structure of flexible object and obtain satisfying results, so the algorithm proposed here depends on this technique.The bottle-neck in most flexible object simulation systems is that time steps must be small to avoid numerical instability and the huge computation cost. Thus the first work we should do is to set up a mass-spring system which is based on dynamics of rigid object, linear spring mechanics and computer graphics. The second and the most important portion in this paper is to detail and analyze a new technique that is used to enable large step and alleviate computation cost. The new technique includes three sides. No.1, an implicit integration method named trapezium formula is introduced to enforce constraints on individual cloth particle. No.2, a fast simulation technique is proposed to approximate the filtering effects of the implicit method in order to alleviate the heavy computation brought by the implicit integration method. No.3, an algorithm to dynamically regulate the time step is detailed. The last work in this paper is to implement the model algorithm on PC and analyze the results.The resulting simulation system is significantly faster than previous cloth simulation systems in the literature. Our experiments show that approximated method produces satisfying animation results in a real-time environment.