有限元方法在变形曲线曲面造型中的应用

APPLICATION OF FINITE ELEMENT METHOD IN DEFORMABLE CURVE AND SURFACE MODEL

变形曲线曲面造型方法是将CAGD中参数化几何描述方法与某些力学原理相结合，自动确定曲线曲面的各种控制参数，使之满足给定的几何约束条件，克服局部修改和整体光顺的矛盾，可用于构造具有复杂形状的物体．在曲线曲面插值、光顺和光滑拼接，以及N边域构造方面有优越性．基于能量函数的变形模型是由能量函数、几何约束和外部载荷定义的变分问题．应用有限元技术求解可得变形曲线曲面．本文对应用有限元方法时的一些关键技术，如有限元网格的生成、约束条件的添加等问题进行了讨论．最后给出了N边域构造方面的几个应用实例．

The deformable model is based on both parametrically described geome-try and energy minimization algorithm, the curve or surface automatically assumes a shape with minimized energy function under the user defined geometric con-straints and loads. This automatic adjustment mimics the behavior of physical me-dia and can mediate the contradictory of local shape manipulation and global fair-ness. The applications in curve and surface interpolation, smooth joining, fairing and N-sided patches demonstrate that the new method has a great advantage. The modeling of energy-based deformable curve and surface is defined by energy func-tion, geometric constraints and external loads. Deformable curve and surface are formed by using finite element method to solve the variational problem. Some im-portant issues, such as generation of mesh and treatment of constraints, are dis-cussed in applying finite element technology. Several examples of N-sided patches construction are given.