三角域上三次Bernstein-Bézier参数曲面的扩展

Extension of the Cubic Bernstein-Bézier Surfaces over the Triangular Domain

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.