带有形状参数的B啨zier三角曲面片  

Bézier Triangular Patch with a Shape Parameter

作　　者：吴晓勤[1] 韩旭里[1] 

机构地区：[1]中南大学数学科学与计算技术学院

出　　处：《计算机辅助设计与图形学学报》2006年第11期1735-1740,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：湖南省教育厅资助项目(04C215)

摘　　要：给出了含有参数的二元(n+1)次多项式基函数,是三角域上二元n次Bernstein基函数的扩展;分析了该组基的性质并定义了带有形状参数的(n+1)次B啨zier三角曲面片·该曲面不仅具有n次B啨zier三角曲面片的特性,而且具有形状的可调性;其参数有明确的几何意义,参数越大,曲面越逼近控制网格;当参数为0时,曲面可退化为n次B啨zier三角曲面片·A class of bivariate polynomial weight function of degree （ n ＋ 1） with a parameter is presented in this paper. They are an extension of bivariate n-degree Bernstein basis functions. Properties of this new basis are analyzed and the （n ＋ 1）-degree triangular Bézier surface with a shape parameter is defined based on them. The surface not only inherits the most properties of n-degree triangular Bézier surface, but also can adjust itself shape through changing the value of parameter. And it is endowed the property of geometry. The larger is the parameter, the more approaches the surface to the control net. When parameter vanishes, the surface degenerates to n-degree triangular Bézier surface.

关 键 词：BÉZIER 曲面 三角域 形状参数 曲面设计 De CASTELJAU算法 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]