GB-spline curves can be considered as the generalization of B-spline curve incorporating a shape parameter into the polynomial basis functions. The geometric effect of the alteration of the shape parameter is discussed in this paper, including constrained shape control of the curve.

Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline “interpolation” (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the Lp-error for adaptive approximation by harm...

Non-polynomial spline is used for solution of the tenth-order linear boundary value problems. We obtained the classes of numerical methods for a specific choice of the parameters involved in non-polynomial spline. The end conditions consistent with the boundary value problems are derived. Truncation errors are given. A new approach convergence analysis of the presented methods is discussed. Two...

This is a study concerning the identification of the heterogeneous flexural rigidity of a beam governed by the steady-state Euler-Bernoulli fourth order ordinary differential equation. We use the method of Variational Imbedding (MVI) to deal with the inverse problem for the coefficient identification from over-posed data. The method is identifying the coefficient by approximating it with a piec...

We present a new approach to the construction of piecewise polynomial or rational C k-spline surfaces of arbitrary topological structure. The basic idea is to use exclusively parametric smoothness conditions, and to solve the well known problems at extraordinary points by admitting singular parametrizations. The smoothness of the spline surfaces is guaranteed by specifying a regular smooth re-p...

When optimizing the performance of constrained robotic system, the motion trajectory plays a crucial role. In this research the motion planning problem for systems that admit a polynomial description of the system dynamics through differential flatness is tackled by parameterizing the system’s so-called flat output as a polynomial spline. Using basic properties of B-splines, sufficient conditio...

In this paper a method for interpolating planar data points by cubic G splines is presented. A spline is composed of polynomial segments that interpolate two data points, tangent directions and curvatures at these points. Necessary and sufficient, purely geometric conditions for the existence of such a polynomial interpolant are derived. The obtained results are extended to the case when the de...

This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for “...