三角域上带两个形状参数的Bézier曲面的扩展

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.

Extension of Bézier Surfaces with Two Shape Parameters over the Triangular Domain

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 1the 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.