基于Bernstein函数类的Bezier曲面类  

A Class of Bezier Surfaces Based on Bernstein Function Class

作　　者：严兰兰[1] 梁炯丰[2] 

机构地区：[1]东华理工大学数学与信息科学学院,抚州344000 [2]东华理工大学土木与环境工程学院,抚州344000

出　　处：《计算机与数字工程》2009年第1期6-10,31,共6页Computer & Digital Engineering

基　　金：东华理工大学校长基金资助项目(编号:DHXK0808;DHXK0828)资助

摘　　要：为了进一步丰富Bezier曲面理论,以及克服原有Bezier曲面理论中的一些不足,在梁锡坤提出的Bernstein函数类的基础上,对基于该类函数的Bezier曲面类的生成方法进行了研究。并给出了两种具体的Bezier曲面类曲面,这两种曲面是基于有理形式调配函数,即RB函数的实用曲面,称之为RB曲面和附权RB曲面。重点研究了RB曲面和附权RB曲面的表示方法和有关性质,同时还分析了这两种曲面之间以及与Bezier曲面之间的关系。得到了较好的结果,使Bezier曲面理论更加完善。In order to enrich and overcome some shortages of the rational theory of Bezier surfaces, a new class of Bezier surfaces based on the Bernstein function class which presented by Liang Xikun is studied. Two kinds of specific sur-faces of Bezier surface class are given. These two kinds of surfaces are very practical, which based on the rational form RB function. They are flexible and convenient in practical application. We call them RB surface and weighted RB surface. The representation and properties of these two kinds of surfaces are chiefly studied. At the same time, the relationship among RB surface and weighted RB surface and the rational Bezier surface is analyzed. In the end, some good conse- quence are obtained, this makes the theory of rational Bezier surfaces more perfect.

关 键 词：曲线曲面造型 Bernstein函数类 Bezier曲面类 RB函数 RB曲面 权因子 正则参数变换 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]