摘要
给出了三角域上带双参数λ1,λ2的类三次Bernstein基函数,它是三角域上三次Bernstein基函数的扩展.分析了该组基的性质并定义了三角域上带有两个形状参数λ1,λ2的类三次Bernstein-Bézier(B-B)参数曲面.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λ1,λ2取特殊的值时,可分别得到三次Bernstein基函数及三次B-B参数曲面以及参考文献中所定义的类三次Bernstein基函数及类三次B-B参数曲面.由实例可知,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 two shape parameters λ1 and λ2 is presented, which is an extension of the cubic Bernstein basis functions defined over the triangular domain： Properties of this new basis are analyzed and the quasi-cubic-B-B parametric surfaces with two shape parameters λ1 and λ2 over the triangular domain is defined based on them. The surfaces＇ properties are similar with the cubic B-B parametric surfaces. In particular, when λ1 and λ2 choose the particular numbers, they degenerate to the cubic Bernstein basis functions and the cubic B-B parametric surfaces individually; we can also get the quasi-cubic-Bernstein basis functions and the quasi-cubic-B-B parametric surfaces defined in the documents by changing the shape parameters. The examples indicate the shape of the surfaces can be adjusted by changing the values of the shape parameters.
出处
《大学数学》
北大核心
2008年第5期58-62,共5页
College Mathematics
基金
合肥工业大学校基金(061007F)
