带约束条件的张量积Bézier曲面最佳降多阶  

The Constrained Optimal Multi-degree Reduction of Tensor Product Bézier Surfaces

作　　者：周联[1] 王国瑾[2] 

机构地区：[1]浙江大学数学系计算机图象图形研究所,杭州310027 [2]浙江大学CAD&CG国家重点实验室,杭州310027

出　　处：《计算机辅助设计与图形学学报》2009年第8期1054-1060,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60873111);国家"九七三"重点基础研究发展计划项目(2004CB719400)

摘　　要：为了交换和存储不同造型系统中的数据,提出一种张量积Bézier曲面带约束条件的一次降多阶算法.该算法在保角点高阶插值情形下,利用原曲面顶点数组的降维方法和最小二乘法给出了Bézier曲面的最佳降多阶逼近;在给定降阶曲面的4条边界曲线的情形下,利用最小二乘法,对原曲面减去降阶曲面的4条边界曲线后所得到的新曲面进行无约束最佳降阶逼近;将保边界插值的降阶方法应用于拼接曲面,所得到的降阶曲面为整体C0连续.数值实验和逼近理论表明,文中算法比其他算法的精度高、效率高.To transfer and store the data in different modeling systems, an optimization algorithm for multi-degree reduction of tensor product Bezier surfaces is proposed with some restrained conditions. Firstly, by interpolating four corners of high degree, the optimal multi-degree reduction of Bezier surfaces is achieved by applying dimension reduction method in surface control points in a least squares minimization manner. Secondly, by interpolating four boundary curves with a degree-reduced surface, the optimal degree reduction of the surface is obtained by least-squares subtracting the degree-reduced surface from the original surface. After using the degree reduction to the piecewise surfaces with the interpolation conditions of boundary curves, the resulting piecewise approximating surfaces are globally CO. Numerical examples and theoretical approximation results suggest that the proposed method is more precise and efficient when compared to previous methods.

关 键 词：BÉZIER曲面 降阶 约束条件 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]