The construction of weighted extended B-splines (web-splines), as recently introduced by the authors and J. Wipper for uniform knot sequences, is generalized to the nonuniform case. We show that web-splines form a stable basis for splines on arbitrary domains in R which provides optimal approximation power. Moreover, homogeneous boundary conditions, as encountered frequently in finite element a...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...

Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (J. Roy. Statist. Soc. Set. B 40 (1978) 364-372; 45 (1983) 133-150) showed that smoothing splines are also Bayes estimates and used the corresponding prior model to derive interval estimates for the regression function. Although the interval estimates work well on a global basis, they can have poor local...

Abstract Multivariate basis splines (B‐splines) and Non‐uniform rational B‐splines (NURBS) lack adaptivity due to their tensor product structure. Truncated hierarchical (THB‐splines) provide a solution for this. THB‐splines organize the parameter space into structure, which enables efficient approximation representation of functions with different levels detail. The truncation mechanism ensures...

Introduction: The Shallow Radar instrument (SHARAD) on the Mars Reconnaissance Orbiter (MRO) has been successful at penetrating into icy deposits [1-3], but most of the rocky units are opaque to SHARAD. The main exceptions to this are the youngest major volcanic surfaces, Cerberus Fossae 2 and 3 units and Amazonis Planitia 2 north unit [4]. We suggest that these units have low radar loss becaus...

Received (Day Month Year) Revised (Day Month Year) Communicated by (xxxxxxxxxx) Fractional B-splines are a natural extension of classical B-splines. In this short paper, we show their relations to fractional divided differences and fractional difference operators , and present a generalized Hermite-Genochi formula. This formula then allows the definition of a larger class of fractional B-splines.

In this paper we consider polynomial splines with equidistant nodes which may grow as O|x|. We present an integral representation of such splines with a distribution kernel where exponential splines are used as basic functions. By this means we characterize splines possessing the property that translations of any such spline form a basis of corresponding spline space. It is shown that any such ...

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...

We demonstrate that non-separable box splines deployed on body centered cubic lattices (BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop the linear and quintic box splines using a piecewise polynomial (pp)-form as opposed to their currently known basis (B)-form. The pp-form lends itself to efficient evaluation methods such as de Boor’s algorithm for spli...

In this paper we consider spaces of bivariate splines of bi–degree (m,n) with maximal order of smoothness over domains associated to a two–dimensional grid. We define admissible classes of domains for which suitable combinatorial technique allows us to obtain the dimension of such spline spaces and the number of tensor–product B–splines acting effectively on these domains. Following the strateg...