In this paper we consider discrete splines S(j), j ∈ Z, with equidistant nodes which may grow as O(|j|s) as |j| → ∞. Such splines are relevant for the purposes of digital signal processing. We give the definition of discrete B-splines and describe their properties. Discrete splines are defined as linear combinations of shifts of the B-splines. We present a solution to the problem of discrete sp...

This paper presents a new kind of splines, called non-uniform algebraic-trigonometric B-splines (NUAT B-splines), generated over the space spanned by {1, t, . . . , tk−3, cos t, sin t} in which k is an arbitrary integer larger than or equal to 3. We show that the NUAT B-splines share most properties of the usual polynomial B-splines. The subdivision formulae of this new kind of curves are given...

Homogeneous simplex splines, also known as cone splines or mul-tivariate truncated power functions, are discussed from a perspective of homogeneous divided diierences and polar forms. This makes it possible to derive the basic properties of these splines in a simple and economic way. In addition, a construction of spaces of homogeneous simplex splines is considered, which in the non-homogeneous...

We study properties of spherical Bernstein-Bézier splines. Algorithms for practical implementation of the global splines are presented for a homogeneous case as well as a non-homogeneous. Error bounds are derived for the global splines in terms of Sobolev type spherical semi-norms. Multiple star technique is studied for the minimal energy interpolation problem. Numerical summary supporting theo...

This paper presents an implementation framework for spline spaces over T-meshes (and their d-dimensional analogs). The aim is to share code between the implementation of several spline spaces. This is achieved by reducing evaluation to a generalized Bézier extraction. The approach was tested by implementing hierarchical B-splines, truncated hierarchical B-splines, decoupled hierarchical B-splin...

We review the theory of homogeneous splines and their relationship to special rational splines considered by J. SS anchez{Reyes and independently by P. de Casteljau who called them focal splines. Applying an appropriate duality, we transform focal splines into a remarkable class of rational curves with rational oosets. We investigate geometric properties of these dual focal splines, and discuss...

We review the theory of homogeneous splines and their relationship to special rational splines considered by J. SS anchez{Reyes and independently by P. de Casteljau who called them focal splines. Applying an appropriate duality, we transform focal splines into a remarkable class of rational curves with rational oosets. We investigate geometric properties of these dual focal splines, and discuss...

Piecewise L-splines are generalizations of L-splines, in the sense that they satisfy different differential equations in different mesh intervals. Prenter attempted in [P.M. Prenter, Piecewise L-Splines, Numer. Math. 18 (2) (1971) 243–253] to obtain results on piecewise L-splines by generalizing the results of Schultz and Varga on L-splines in [M.H. Schultz, R.S. Varga, L-Splines, Numer. Math. ...