AS++ T-splines: arbitrary degree, nestedness and approximation (Q2049920)

NURBS (non-uniform rational B-splines) and similar approximation methods such as the so-called T-splines are important methods in the applications of numerical analysis. In this article, T-splines are analysed, and the important properties such as recursive definitions and convergence orders considered. Nestedness features and recursive computation by ``refinement equations'' are especially important because they support numerical stability and efficient evaluations. The research on T-splines started with the cubic spline case, and this approach is generalised in this article. Several numerical examples are provided and approximation orders of optimal approximation are computed.