A simple approach to the basic functions for b-spline curves

摘要

B-Splines are piecewise polynomial curves.Each knot only affects locally some segments. The basic functions. N_i.k have been studied in detail for both non-uniform and uniform cases [1,2,3,4]. In this paper, a simple method to obtian these functions for a uniform knot sequence is given. In the first section of this paper, a step by step derivation of these functions is presented. In the second section a generalization is attempted for any degree. Finally, an extension to non-uniform case is discussed.