摘要
文章对已有的含2个参数的单变量基函数,即αβ-B基进行了深入的研究,得出了基函数的显式表示,以及基函数与Bernstein基之间的关系,探讨了由之定义的曲线与Bézier曲线之间的关系,以及曲线的递推求值算法;定义了相应的四边域上的张量积曲面,给出了曲面与张量积Bézier曲面之间的关系;并将αβ-B基推广至三角域,定义了相应的双变量基函数,给出了该基函数的显式表示,以及与Bernstein多项式之间的关系;分析了该双变量基函数的性质,定义了相应的三角域曲面,讨论了该曲面与Bernstein-Bézier曲面之间的关系,以及曲面的递推求值算法。
The existing univariate basis function which studied. The explicit expression of the basis function is contains two parameters, i. e. αβ-B,basis, is obtained. The connection of the basis function with the Bernstein basis is given. The connection of the corresponding curve with the Bezier curve is discussed. The recursive evaluation algorithm of the curve is also given. The tensor product surface over the rectangular domain based on the univariate basis function is defined. The connection of this surface with the tensor product Bezier surface is given. Then the αβ-B basis is extended to the triangular domain, and the corresponding bivariate basis function is defined. The explicit expression and the properties of the bivariate basis function and its connection with the Bernstein polynomial are analyzed. The corresponding surface over the triangular domain is defined. The connection of the new triangular surface with the Bernstein-Bezier surface and the recursive evaluation algorithm of the surface are discussed.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第5期625-631,共7页
Journal of Hefei University of Technology：Natural Science
基金
国家自然科学基金资助项目(11261003)
