一类柔软物体悬垂的实时模拟技术

Real-Time Simulation Technique for a Kind of Flexible Objects

使用质点—弹簧 ( MS)模型来表示一类柔软物体 (如织物 )可能是一种最简单和直观的建模方案 .显式尤拉方法是使用 MS模型来产生动态效果的最简单方法 ,但该方法的严重缺陷在于算法本身的不稳定性 .隐式积分方法是一种可行的算法 ,但关键要寻找一种有效的方法求解引入的大型线性系统 .本文提出了一种基于雅可比迭代法的隐式数值积分算法 ,通过理论证明和分析 ,该算法稳定地更新 n个质点的状态所需时间复杂度为 O( n) ,较已有的隐式积分算法有了很大的改进 .

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.