A Cox-de Boor-type recurrence relation for C1 multi-degree splines

Multi-degree splines are piecewise functions comprised of polynomial segments of different degrees. A subclass of such splines, that we refer to as C1 MD-splines, is featured by arbitrary continuity between pieces of same degree and at most C1 continuity between pieces of different degrees. For these spline spaces a B-spline basis can be defined by means of an integral recurrence relation, as an instance of the more general construction in Beccari et al. (2017). In this paper, we provide efficient formulas for evaluating C1 MD-splines and their derivatives, akin to the classical B-spline recurrence relations. Furthermore we derive algorithms for geometric design, including knot insertion and local degree elevation. Finally we demonstrate the utility of these splines, not only for geometric modeling, but also for graphical applications, discussing in particular the advantages for modeling and storing vector images.