B-样条函数极小曲面造型  

Approximating to Nonparameterzied Minimal Surface with B-Spline Surface

作　　者：满家巨[1,2] 汪国昭[3] 

机构地区：[1]湖南师范大学计算机科学系 [2]浙江大学数学系计算机图象图形研究所,浙江杭州310027 [3]浙江大学数学系计算机图象图形研究所

出　　处：《软件学报》2003年第4期824-829,共6页Journal of Software

基　　金：国家自然科学基金;国家重点基础研究发展规划(973)~~

摘　　要：极小曲面在建筑、航空、轮船制造等领域有着重要应用,但由于极小曲面表示复杂,给实际应用带来了很大的困难.研究了具有给定边界的极小曲面的B-样条函数曲面逼近.基于非线性约束优化方法和有限单元方法,求极小曲面方程的近似解.在算法中使用数值延拓方法,使非线性问题的初值选择问题自动化,同时,使用一个简单的线性化策略对非线性问题进行线性化.给出了几个数值结果.The minimal surfaces have been extensively employed in many areas such as architecture, aviation, ship manufacture, and so on. However, the complexity of the minimal surface equation prevents people from modeling the minimal surface in CAD/CAGD. In this paper, based on the nonlinear programming and the FEM (finite element method), the approximation to the solution of the minimal surface equation bounded by B閦ier or B-spline curves is investigated. A global method, which is called numerical extension method, is appealed to in the whole iterative process and linearize the nonlinear finite element system by using a simple iteration. Some numerical results are given in this paper.

关 键 词：B-样条函数 极小曲面造型 CAD CAGD BEZIER曲面 B-样条曲面 数值延拓 有限元 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]