张量积Bézier曲面降多阶逼近的方法  

New Approach to Approximate Multi-degree Reduction of Tensor Product Bézier Surfaces

作　　者：郭清伟[1] 朱功勤[2] 

机构地区：[1]中国科学技术大学数学系,合肥230026 [2]合肥工业大学理学院,合肥230009

出　　处：《计算机辅助设计与图形学学报》2004年第6期777-782,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金 ( 10 1710 2 6)资助

摘　　要：提出根据原张量积B啨ｚｉｅｒ曲面Ｐｎ ,m(u ,v)与降多阶张量积B啨ｚｉｅｒ曲面Ｑｎ1 ,m1 (u ,v) (n1≤n - 1,m1≤m -1)在最小二乘范数下的距离函数在单位正方形 [0 ,1]× [0 ,1]上取最小值 ,得到张量积B啨ｚｉｅｒ曲面降多阶逼近的方法 ,以及用矩阵表示的降多阶张量积B啨ｚｉｅｒ曲面Ｑｎ1 ,m1 (u ,v)的控制顶点 { qij} n1 ,m1 i=0 ,j=0 的显式表示式 在降多阶过程中 ,分别考虑了带角点高阶插值条件和不带角点插值条件的情形 数值例子显示 。An approach is presented through minimizing the distance function between P n,m(u,v) and Q n 1,m 1(u,v)(n 1≤n-1,m 1≤m-1) over unit square [0,1]×[0,1] in the sense of least squares normal (L 2),which gives the explicit representation of control points {q ij} n 1,m 1 i=0,j=0 of the reduced multi-degree tensor product Bézier surface Q n 1,m 1(u,v). During the multi-degree reduction process, we also consider two cases, one has the constraint of high-order interpolations over corners and another without any constraint. Examples show that the proposed approach has better approximation of the reduced surfaces than that of current methods.

关 键 词：张量积BÉZIER曲面 降多阶 角点插值 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]