This paper proposes a fast method for the calculation of exponential B-splines sampled at regular intervals. This algorithm is based on a combination of FIR and IIR filters which enables a fast decomposition and reconstruction of a signal. When complex values are selected for the parameters of the exponentials, complex trigonometric functions are obtained. Only the real part of these functions ...

This paper describes an algebraic construction of bivariate interpolatory subdivision masks induced by three-directional box spline subdivision schemes. Specifically, given a three-directional box spline, we address the problem of defining a corresponding interpolatory subdivision scheme by constructing an appropriate correction mask to convolve with the three-directional box spline mask. The p...

Stitching or merging B-spline curves is a frequently used technique in geometric modeling, and is usually implemented in CAD-systems. These algorithms are basically numerical interpolations using the least squares method. The problem, how to replace two or more curves which are generated separately and defined as B-spline curves, has well functioning numerical solutions, therefore, relatively f...

In this paper sixth order boundary value problems is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. The septic B-splines constitute a basis for the space of septic polynomial splines. In the method, the basis functions are redefined into a new set of basis functions which in number match with the number of selected co...

In this paper we prove that there exists a unique positive symmetrical univariate B-spline with minimal support. It is obtained as linear combination of a minimal number of successive classical B-splines with multiple knots in the space, S d , of cardinal polynomial splines of class C and degree d. Next, we show that the approximation order in the space generated by the integer translates of th...

Hierarchical B-spline networks consist of multiple B-spline networks assembled in different level or cascade architecture. To identify the hierarchical B-spline networks and select important input features for each sub-B-spline network automatically, a predefined instruction/operator set was used. The structures of hierarchical B-spline networks were created and evolved by using Probabilistic I...

A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented in this work. Speciically, the convolution between the B-spline coeecients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% o...

We present a fast method that adaptively approximates large-scale functional scattered data sets with hierarchical B-splines. The scheme is memory efficient, easy to implement and produces smooth surfaces. It combines adaptive clustering based on quadtrees with piecewise polynomial least squares approximations. The resulting surface components are locally approximated by a smooth B-spline surfa...

This paper deals with the use of trigonometric splines (also call Schoenberg’s polynomials) in order to increasing the performances of a nonlinear closed-loop system. In the first part, it is recalled that for linear systems, the couple ”setting time/overshoot” can be largely improved if a path planning is used instead of a classical step input. The concept of trigonometric splines is then intr...