Knot intervals and multi-degree splines

This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for “multi-degree”). MD-splines are a generalization of B-spline curves in that if all curve segments in an MD-spline have the same degree, it reduces to a B-spline curve. The paper focuses on MD-splines of degree 1, 2, and 3, as well as degree 1 and n. MD-splines have local support, obey the convex hull and variation diminishing properties, and are at least C, where n is the smaller of the degrees of two adjoining curve segments.