Explicit representations of changeable degree spline basis functions

Abstract

Changeable degree spline (CD-spline for short) basis functions, defined by an iterative integral method, are extensions of B-spline basis functions. A CD-spline basis function is a piecewise function made up of polynomials of different degrees. In this paper, we will give the explicit representations of CD-spline basis functions, from which the spanned linear space can be seen clearly. Our method is also feasible for the explicit representations of the other basis functions given in analogous integral ways.