In this paper, we construct a matrix, which transforms a generalized C-Bézier basis into a generalized uniform algebraic-trigonometric B-spline (C-B-spline or UAT B-spline) basis. We also show that it is a totally positive matrix and give a normalized B-basis of the generalized UAT B-splines.  2005 Elsevier B.V. All rights reserved.

In this paper we consider equidistant polynomial splines S(x) which may grow as O|x|s. We present an integral representation of such splines with a distribution kernel. This representation is related to the Fourier integral of slowly growing functions. The part of the Fourier exponentials herewith play the so called exponential splines by Schoenberg. The integral representation provides a flexi...

The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effecti...

We establish rigorously the fundamental nesting behavior of T-spline spaces in terms of the topology of the T-mesh. This provides a theoretical foundation for local refinement algorithms based on analysis-suitable T-splines and their use in isogeometric analysis. A key result is a dimension formula for smooth polynomial spline spaces defined over the Bézier mesh of a T-spline.

Let φ be an orthonormal scaling function with approximation degree p−1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by f̄n = f ∗Bn (n = 1, 2, . . . ) possess higher approximation order, p+n−1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function sy...

Abstract. We describe and demonstrate an arrow notation for deriving box-spline subdivision schemes. We compare it with the z-transform, matrix, and mask convolution methods of deriving the same. We show how the arrow method provides a useful graphical alternative to the three numerical methods. We demonstrate the properties that can be derived easily using the arrow method: mask, stencils, con...

The paper presents the differential quadrature method (DQM) based on a modified spline interpolation and the application of the method in vibration analysis of laminated, composite shells. The goal of the modification of the spline interpolation is to improve the rate of convergence and preserve the stability of the method. The modification changes the definition of the end conditions for the s...

It is proved that, among all nonnegative bases of its space, the B-spline basis is optimally stable for evaluating spline functions.