The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interele...

In this paper, we contribute a new B-spline based interval field decomposition method as non-probabilistic approach that takes into account local effects in modelling. With basis functions, the formulation is highly intuitive and easy to construct. The computational efficiency outperforms traditional method. explicit expression of proposed facilitates use optimisation methods determining bounds...

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute refinement mask of B-splines any order in case general scaling factor. Our is solely derived from reproduction properties satisfied by splines it does not require explicit construction or evaluation basis functions. The second part discusses factorization B-spline masks terms a...

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is crucial to obtain desirable results in these areas. This paper considers the injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric inte...

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory—including some new extensions for fractional orders—in a se...

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory—including some new extensions for fractional orders—in a se...

B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the...

We study the general problem of computing an obstacle-avoiding path that, for a prescribed weight, minimizes the weighted sum of a smoothness measure and a safety measure of the path. We consider planar curvaturecontinuous paths, that are functions on an interval of a room axis, for a point-size vehicle amidst obstacles. The obstacles are two disjoint continuous functions on the same interval. ...

Keywords: Differential quadrature method Hyperbolic telegraph equation Modified B-spline basis functions Thomas algorithm a b s t r a c t The present paper uses a relatively new approach and methodology to solve second order two dimensional hyperbolic telegraph equation numerically. We use modified cubic B-spline basis functions based differential quadrature method for space discretization that...