摘要
给出了三角域上带参数的类三次Bernstein基函数,它是三角域上三次Bernstein基函数的扩展.基于给出的基函数,提出一种建立三角域上带形状参数的类三次Bernstein-Bézier(B-B)参数曲面的生成方法.该基函数及参数曲面分别具有与三次Bernstein基函数及三次B-B参数曲面类似的性质,当形状参数取值为1时,它们分别退化为三次Bernstein基函数和三次B-B参数曲面.研究表明,通过改变形状参数的取值,可以调整曲面的形状.
A class of quasi-cubic-Bernstein basis functions with a single parameter is presented, which is an extension of the cubic Bernstein basis functions defined over the triangular domain. Based on the introduced functions, we propose a method to produce the quasi-cubic-B-B parametric surfaces defined over the triangular domain with a single shape parameter. The surfaces＇ properties are similar with the cubic B- B parametric surfaces. In particular, when the shape parameter equals 1, they degenerate to the cubic B-B parametric surfaces. By changing the shape parameter, we can get surfaces with different shapes in invariable control net.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2006年第9期1403-1407,共5页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(60473130)
国家重点基础研究发展规划项目(2004CB318000)
