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...

Neural fields are spatially continuous state variables described by integro-differential equations, which are well suited to describe the spatiotemporal evolution of cortical activations on multiple scales. Here we develop a multi-resolution approximation (MRA) framework for the integro-difference equation (IDE) neural field model based on semi-orthogonal cardinal B-spline wavelets. In this way...

This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation (PIDE) with a weakly singular kernel. Cubic trigonometric B-spline (CTBS) functions are used interpolation in both methods. The first method is CTBS based collocation which reduces PIDE to an algebraic tridiagonal system linear equations. other differentia...

A method for generating an interpolation closed G arc spline on a given closed point set is presented. For the odd case, i.e. when the number of the given points is odd, this paper disproves the traditional opinion that there is only one closed G arc spline interpolating the given points. In fact, the number of the resultant closed G arc splines fulfilling the interpolation condition for the od...

In this paper it is presented another method to determine the coefficients in B-spline interpolation. The problem is resolved in the context of generalized spline interpolation. To determine the coefficients from the input samples is first step for performing the interpolation. The operation is done by using also the values of the second derivative for the input signal. The coefficients are use...

In this paper we present a new method for the model of interpolation sweep surfaces by the C-continuous generalized quasicubic interpolation spline. Once given some key position, orientation and some points which are passed through by the spine and initial cross-section curves, the corresponding sweep surface can be constructed by the introduced spline function without calculating control point...

The usefulness of fuzzy input fuzzy output functions and their interpolation/approximation by different operators in fuzzy control motivate their deeper theoretical study. We obtain some properties of fuzzy B-spline series such as variation and uncertainty diminishing property. We also propose spline approximation of fuzzy input fuzzy output functions. Key–Words: Fuzzy numbers, Fuzzy splines, A...

Recursive evaluation procedures based on spherical linear interpolation and stationary subdivision algorithms based on geodesic midpoint averaging are used to construct the analogues on spheres of arbitrary dimension of Lagrange and Hermite interpolation and Bezier and B-spline approximation.

The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion formula is applied to derive a generalized two–scale relation for B-splines with multiple knots. Furthermore, the structure of the corresponding autocorrelation symbol is investigated. In particular, it can be observed that the solvability of the cardinal Hermite spli...