Making the Oslo Algorithm More Efficient

The Oslo Algorithm is a general method for adding knots to a B-spline curve or tensor product B-spline surface. The method provides a framework in computer aided geometric design for both manipulating and rendering spine curves and surfaces, and is derived from properties of discrete B-splines. In this paper we prove that all discrete B-splines which are nonzero at a particular point can in general be considered as lower order discrete B-splines on a subset of the knots. We also give necessary and sufficient conditions for a discrete B-spline to be a continuous function of its parameters. These results are used to improve on the original Oslo algorithms.