B‐spline based on vector extension improved CST parameterization algorithm

Abstract

In this paper, the vector extension operation is proposed to replace the de Boor‐Cox formula for a fast algorithm to B‐spline basis functions. This B‐spline basis function based on vector extending operation is implemented in the class and shape transformation (CST) parameterization method in place of the traditional Bézier polynomials to enhance the local ability of control and accuracy to represent an airfoil shape. To calculate the k‐degree B‐spline function's nonzero values, the algorithm can improve the computing efficiency by 2k+1 times.