Stable Simplex Spline Bases for $$C^3$$ C 3 Quintics on the Powell–Sabin 12-Split

A Hermite interpolatory subdivision scheme for C2-quintics on the Powell-Sabin 12-split

In order to construct a C1-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell-Sabin 12-split. It has been shown previously that the corresponding spline surface can be plotted quickly by means of a Hermite subdivision scheme [5]. In this paper we introduce a nodal macroelement on the 12-split...

On Stable Local Bases for Bivariate Polynomial Spline Spaces

Stable locally supported bases are constructed for the spaces S r d (4) of polynomial splines of degree d 3r + 2 and smoothness r deened on trian-gulations 4, as well as for various superspline subspaces. In addition, we show that for r 1, it is impossible to construct bases which are simultaneously stable and locally linearly independent. x1. Introduction This paper deals with the classical sp...

Stable Bases of Spline Wavelets on the Interval

Following the approach of Chui and Quak, we investigate semi-orthogonal spline wavelets on the unit interval [0, 1]. We give a slightly different construction of boundary wavelets. As a result, we are able to prove that the inner wavelets and the newly constructed boundary wavelets together constitute a Riesz basis for the wavelet space at each level with the Riesz bounds being level-independen...

Non-Homogeneous Spline Bases for Approximation on the Sphere

Einladung Zum Kolloquium Simplex Splines for the Powell-sabin 12-split