Non-uniform subdivision for B-splines of arbitrary degree

We present an efficient algorithm for subdividing non-uniform B-splines of arbitrary degree in a manner similar to the Lane–Riesenfeld subdivision algorithm for uniform B-splines of arbitrary degree. Our algorithm consists of doubling the control points followed by d rounds of non-uniform averaging similar to the d rounds of uniform averaging in the Lane–Riesenfeld algorithm for uniform B-splines of degree d. However, unlike the Lane–Riesenfeld algorithm which follows most directly from the continuous convolution formula for the uniform B-spline basis functions, our algorithm follows naturally from blossoming. We show that our knot insertion method is simpler and more efficient than previous knot insertion algorithms for non-uniform B-splines.