This paper is concerned with the description of an algorithm for generating the B-nets of box splines and an algorithm based on subdivision of these B-nets for graphically displaying spline surfaces on a three-or four-directional mesh. The combination of these two algorithms is shown to compare favorably over the other existing algorithms for this purpose. 0 1 x1. Introduction It is well known ...

Objectives. Methods for spline approximation of a sequence points in plane are increasingly used various disciplines. A is defined as single-valued function consisting known number repeating elements, which the most widely polynomials. When designing routes linear structures, it necessary to consider problem with an unknown elements. An algorithm implemented solving this when longitudinal profi...

Using new properties of dual functions, we show that the method of constructing the dual bases recently presented in [P. Woźny, J. Comput. Appl. Math. 245 (2013), 75–85] can be significantly simplified. Next, we propose a simple algorithm of constructing the dual B-spline functions, which can be useful in solving some approximation problems related to numerical analysis or computer graphics.

In the Fourier series approximation of real functions discontinuities of the functions or their derivatives cause problems like Gibbs phenomenon or slow uniform convergence. In the case of a nite number of isolated discontinuities the problems can be to a large extend recti ed by using periodic splines in the series. This modi ed Fourier series (Spline-Fourier series) is applied to the numerica...

The estimation of functions with varying degrees smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose LABS (L\'{e}vy Adaptive B-Spline regression) model, an extension LARK models, for smoothness. model B-spline bases as generating kernels. basis consists piecewise k degree polynomials k-1 continuous derivatives and can express systematically By...

As is now well known for some basic functions φ, hierarchical and fast multipole-like methods can greatly reduce the storage and operation counts for fitting and evaluating radial basis functions. In particular, for spline functions of the form