For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...

A variety of techniques to facilitate fast graphical display of curves and surfaces for interactive CAGD purposes have been developed, in the past years. Many of these are commonly referred to as subdivision algorithms PI. In this paper we propose a method for subdividing simplex splines, i.e., splines that can be defined over non-regular grid partitions. There is a relatively exhaustive theory...

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...

A quasi-interpolation method for quadratic piecewise polynomials in three variables is described which can be used for the efficient visualization of gridded volume data. We analyze the smoothness properties of the trivariate splines. We prove that the splines yield nearly optimal approximation order while simultaneously its piecewise derivatives provide optimal approximation of the derivatives...

Tile $\mathrm{B}$-splines in $\mathbb R^d$ are defined as autoconvolutions of indicators tiles, which special self-similar compact sets whose integer translates tile the space R^d$. These functions not piecewise-polynomial, however, being direct generalizations classical $\mathrm{B}$-splines, they enjoy many their properties and have some advantages. In particular, exact values Hölder exponents...

In the present paper, we give approximate values of π deduced from the areas of inscribed and circumscribed quadratic and cubic circular splines. Similar results on circular splines of higher degrees and higher approximation orders can be obtained in the same way. We compare these values to those obtained by computing the perimeters of those circular splines. We observe that the former are much...

In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.

In this paper, we introduce the new class of twisted B-splines and study some properties these B-splines. We also investigate system translates wavelets corresponding to