采用多曲线拟合的柔性体建模仿真方法

提出了一种多曲线拟合的数学建模方法，用于在仿真中快速建立柔性物体受力的形变模型。该方法根据柔性体的形变特性将其外形轮廓分为多个部分；然后使用不同的简单曲线拟合各部分轮廓的形状，并通过改变拟合曲线的参数使得曲线形状改变，以此定量仿真出轮廓的受力形变；最后将曲线拼接起来构成物体的整体形变模型。文中讨论了常见的方体和板块体在挤压、拉伸和扭转这三种非常普遍受力下的形变特性，并使用多曲线拟合方法建立了形变模型。多曲线拟合方法虽然在表现精度上存在一定误差，但建模形式简单、计算速度快，为仿真中表现速度与表达精度的矛盾提供了一种有效的解决手段。

A Modeling and Simulation Method for Flexible Object by Using Curve Fitting

A mathematical modeling method using curve fitting is presented to rapidly establish deformation model for flexible object bearing different forces in computer simulation. The modeling method divides the contour of a flexible object into some parts according to its deformation characteristics. Each contour part is then fitted by an appropriate and simple curve so that the deformation of this contour can be simulated through the shape variation of the fitting curve. Therefore, the deformation model of the flexible object is obtained by connecting all the fitting curves. Using the developed modeling method, the paper establishes the deformation models for a cube and a plate under press, stretch and torsion respectively to prove the method＇s efficiency. Although having some errors, the curve fitting method has the advantages of simple implementation and fast computation, so it provides a feasible resolution for the contradiction of representing speed and precision in computer simulation.