【作者】 朱淮冰；

【导师】 金小刚；

【作者基本信息】 浙江大学 ， 计算机应用技术， 2004， 硕士

【摘要】 布料动画模拟是当前图形学界的一个热点研究方向。早期的布料模拟通常用几何方法，模拟质量很差。广泛采用物理方法以后，布料动画技术得到了很大的发展。然而这些技术或者计算效率不高，或者计算速度较快但物理相容性差，模拟的质量不高。造成这个问题的主要原因，是物理方法需要求解一组微分方程，求解过程的稳定性问题使得计算复杂度难以控制。 本文提出了一种基于物理模型的布料动画模拟技术，同时改善了物理模型和改进了数值积分方法，从而达到算法稳定快速的目的。我们充分分析模型的物理原理，引进细长杆的稳定性原理来模拟粒子模型中的压缩和弯曲现象，并将之简化以方便计算。在数值积分上，我们采用只迭代少数次的松弛法的迭代方法计算隐式积分的稀疏线性系统，这个方法比采用共轭梯度法具有更高的效率，并且计算复杂度是线性的。同时，与别的近似隐式法相比，我们的方法又具有更高的精度，并且没有引入别的人工瑕疵导致模拟丧失许多物理真实性。本文的算法既有相当好的模拟效果，物理真实性好，又达到了相当高的速度，可以胜任一些模型规模不是很复杂的情况下的实时动画模拟。由于算法的复杂度是线性的，这使得该算法非常适合大规模模型下的精确模拟。得益于更能体现布料物理特性的模型和隐式积分方法，我们的算法的稳定性非常好。更多还原

【Abstract】 Cloth modeling and animation is a hot topic in computer graphics. In the early stage of cloth modeling, geometry approaches are usually employed, but the results are poor. Since the employment of physically based approaches, cloth animation has gained great progress. However, these methods are usually not very efficient or the physical plausibility is poor. The main problem is that physically based approaches involve numerically solving a differential equation, and the numerical instability limits the time step. Thus, the computation cost is very expensive.In this thesis, an efficient and stable method to animate virtual cloth based on physics model is proposed. The method revises both the physics model and the numerical integration method, so it is very efficient and stable. We employ the theory of column buckling to simulate the compression and bending phenomenon of cloth. To reduce computation, we simplify the compression and bending model to linear spring. To solve the linear equation system in numerical integrating, we employ relaxation method and only a few iterations are needed. This method is more efficient than conjugate gradient one, and can be computed in O(n) time complexity. Compared with other approximation implicit method, our approach has the advantage of stable, accurate and realistic. Experimental results show our method is satisfactory and is efficient enough to simulate middle-scale cloth model in real time. Because our method can be computed in O(n) time complexity, it can be used for large-scale cloth simulation.更多还原