Research of the real-time interpolation based on piecewise power basis functions

Abstract

With the outstanding geometric properties of B-spline, its recursive algorithm has been widely applied in numerical control systems to compute interpolation points and their derivatives. However, some of the B-spline basis functions in the recursive algorithm are computed repeatedly during the numerical control interpolation, which makes the interpolation efficiency greatly deteriorated. To deal with this issue, an effective approach by converting B-spline to piecewise power basis functions is proposed in this article. With the proposed power basis functions, formulas for computing interpolation point and its derivative can be established explicitly. Thus, the repeated computation due to the implicit expression can be avoided. To further improve the real-time interpolation performance, curve subdivision based on the proposed power basis functions is implemented simultaneously. Theoretical analysis shows that the computational complexity of the proposed method can be reduced by 71.1% compared with the DeBoor-Cox algorithm during the computation of interpolation points and their derivatives. Furthermore, the computational complexity of the curve subdivision can be reduced by 64.5%. Experimental results on a two-dimensional butterfly and a three-dimensional pigeon show that the proposed methods can greatly improve the computational efficiency.