B-spline based on vector extension improved CST parameterization algorithm

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 Bezier 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. Using B-spline to improve the CST parameterization algorithm increases the parameterization design space and improves the local control ability of the CST algorithm. The vector expansion method is used to realize the fast evaluation of B-spline, and the calculation efficiency is increased by 2k+1$$ 2k+1 $$ timesimage