T-spline has been recently developed to represent objects of arbitrary shapes using a smaller number of control points than the conventional NURBS or B-spline representations in computer aided design, computer graphics, and reverse engineering. However, existing methods for fitting a T-spline over a point cloud are slow. By shifting away from the conventional iterative fitand-refine paradigm, w...

For orthogonal cardinal spline approximation, closed form expressions of the reproducing kernel and the Peano kernels in terms of exponential splines are proved. Concrete and sharp pointwise error bounds are deduced for low degree splines.

Non-uniform B-spline dictionaries on a compact interval are discussed. For each given partition, dictionaries of B-spline functions for the corresponding spline space are constructed. It is asserted that, by dividing the given partition into subpartitions and joining together the bases for the concomitant subspaces, slightly redundant dictionaries of Bsplines functions are obtained. Such dictio...

The modification of a knot of a B-spline curve of order k generates a family of B-spline curves. We show that an envelope of this family is a B-spline curve defined by the same control polygon, and its order is k −m, where m is the multiplicity of the modified knot. Moreover, their arbitrary order derivatives differ only in a multiplier.  2003 Elsevier Science B.V. All rights reserved.

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and produce sequences of vertices fj and bj respectively. We proposed to analyze a subdivision scheme Js that blends the rules of these two refinement methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a...

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...

A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...

in this paper, we use a third degree b-spline function to construct an approximate solution forthird order linear and nonlinear boundary value problems coupled with the least square method. severalexamples are given to illustrate the efficiency of the proposed technique.