Knot Removal for Tensor Product Splines

Given a spline function as a B-spline expansion the object of knot removal is to remove as many knots as possible without perturbing the spline by more than a specified tolerance. In 1987 Lyche and Marken proposed an efficient knot removal algorithm which determines both the number of remaining knots and their position automatically. In this paper we show how their method can be extended to knot removal techniques for multivariate tensor product splines. We propose a number of new strategies for removing as many knots as possible, and discuss some of the advantages and challenges posed by the special structure of tensor product splines.