A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well known B-splines, play a key role in computer aided geometric designs. Refinable splines have been studied in several papers, most noticably in [7] for integer dilations and [3] for real dilations. There are general characterizations in these papers, but these characte...

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar simplex is introduced, new formulations of smoothness conditions of bivariate quartic C1 splines and quintic C2 ...

Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided differences at the knots. Direct algorithms and recurrence relations are proposed for constructing discrete generalized B-splines (discrete GB-splines for short). Properties of discrete GB-splines and their series are studied. It is shown that discrete G...

In science and engineering there often is a need for the approximation of scattered multi-dimensional data. A class of powerful scattered data approximators are the multivariate simplex B-splines. Multivariate simplex B-splines consist of Bernstein basis polynomials that are defined on a geometrical structure called a triangulation. Multivariate simplex B-splines have a number of advantages ove...

In this paper, we forecast ground level ozone concentrations over the USA, using past spatially distributed measurements and the functional linear regression model. We employ bivariate splines defined over triangulations of the relevant region of the USA to implement this functional data approach in which random surfaces represent ozone concentrations. We compare the least squares method with p...

This paper compares two techniques for the approximation of the offsets to a given planar curve. The two methods are based on approximate conversion of the planar curve into circular splines and Pythagorean hodograph (PH) splines, respectively. The circular splines are obtained using a novel variant of biarc interpolation, while the PH splines are constructed via Hermite interpolation of C boun...

Employing discrete B-splines instead of the Gaussian distribution, we construct an algorithm for the analysis of ionmobility spectrometry profiles. The algorithm is suitable for hardware implementation because the discrete B-splines are supported by a simple digital filter to compute their weighted sum and their correlations with a given signal. Minutely shifted discrete B-splines are deployed ...

Piecewise polynomials of some xed degree and continuously di erentiable upto some order are known as splines or nite elements. Splines are used in applications ranging from image processing, computer aided design, to the solution of partial di erential equations via nite element analysis. The spline tting problem of constructing a mesh of nite elements that interpolate or approximate multivaria...

We describe a new scheme based on quadratic C-splines on type-2 triangulations approximating gridded data. The quasiinterpolating splines are directly determined by setting the BernsteinBézier coefficients of the splines to appropriate combinations of the given data values. In this way, each polynomial piece of the approximating spline is immediately available from local portions of the data, w...

This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span{sinh t, cosh t, tk−3, tk−4, . . . , t,1} in which k is an arbitrary integer larger than or equal to 3. Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of cur...