Real-Time Simulation Technique for a Kind of Flexible Objects

The simplest and most intuitive approach for modeling a kind of flexible objects is possibly the mass-spring (MS) model. The easiest way to create animation with the mass-spring model is the explicit Euler method, but the method has a serious weakness of its instability. The implicit integration method is a possible solution, but the key problem involves finding an efficient technique for solving a large linear system. This paper proposed an implicit technique based on the Jacobi's iteration method. The theoretical demonstration and analysis show that the proposed method meet both the real-time and the stability requirement well. The new method which can update stably the state of n mass points with the time complexity of O(n) has great advantages over the existing implicit integration methods.