Changeable degree spline basis functions

摘要

A B-spline basis function is a piecewise function of polynomials of equal degree on its support interval. This paper extends B-spline basis functions to changeable degree spline (CD-spline for short) basis functions, each of which may consist of polynomials of different degrees on its support interval. The CD-spline basis functions possess many B-spline-like properties and include the B-spline basis functions as subcases. Their corresponding parametric curves, called CD-spline curves, are like B-spline curves and also have many good properties. If we use the CD-spline basis functions to design a curve made up of polynomial segments of different degrees, the number of control points may be decreased.