As a rule, an energy method is widely adopted for b-spline curve smoothing, but this method has the disadvantages such as massive calculation, computation complexity and low efficiency. Compared with the energy method, multi-resolution smoothing approaches nicely overcome these obstacles. Presently, some researches have been conducted on multi-resolution smoothing, but these efforts mainly aime...

The matrix forms for curves and surfaces were largely promoted in CAD. These formulations are very compact to write, simple to program, and clear to understand. They manifest the desired basis as a matrix transformation of the common power basis. Furthermore, this implementation can be made extremely fast if appropriate matrix facilities are available in either hardware or software. Derivatives...

Investigating the Eulerian numbers and uniform B-spline recurrence relations, a connection between Eulerian numbers and B-spline values at knot points is proved, and a relation to inner products of uniform B-splines is shown. This connection allows, with few operations, to evaluate the B-spline curve at domain knots and could be utilized to obtain an easy approximation and representation of B-s...

We propose a new quadrature rule for Cauchy principal value integrals based on quadratic spline quasi-interpolants which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights is g...

The problem of article is cubic spline-interpolation of functions having high gradient regions. It is shown that uniform grids are inefficient to be used. In case of piecewise-uniform grids, concentrated in the boundary layer, for cubic spline interpolation are announced asymptotically exact estimates on a class of functions with an exponential boundary layer. There are obtained results showing...

The natural frequencies of non-uniform beams resting on elastic foundations are numerically obtained using the spline collocation procedure. The spline collocation method is a numerical approach effective at solving partial differential equations. The boundary conditions that accompanied the spline collocation procedure were used to convert the partial differential equations of non-uniform beam...

In this paper a new digital audio watermarking algorithm is proposed based on B-spline approximation. The algorithm takes the advantage of non-uniform B-spline wavelet, namely, the number of low-frequency components can be arbitrarily selected, so, it is very flexible. Meanwhile, it avoids the complex calculations of non-uniform B-spline wavelets. The simulation experiments show that this algor...