The problem of semi-cardinal spline interpolation was solved by Schoenberg exploiting the piecewise polynomial form of the splines. In the present paper, we propose a new construction for the Lagrange functions of semi-cardinal spline interpolation , based on a radial basis and Fourier transform approach. This approach suggests a way of extending semi-cardinal interpolation to polyharmonic spli...

This is an intuitive description of some of the parametric spline formulations that are most prevalent in computer graphics. The intent is to provide a "high-level". descriptive presentation rather than a detailed, rigorous one. The specific teChniques discussed are piecewise Hermite interpolation. spline interpolation. B6zier curves. Bsplines. Beta-splines. and rational splines. The topics of ...

Abstract. In this paper we propose a local spline method for the approximation of the derivative of a function f . It is based on an optimal spline quasi-interpolant operator Q2, introduced in [12]. Differentiating Q2 f , we construct the pseudo-spectral derivative at the quasi-interpolation knots and the corresponding differentiation matrix. An error analysis is proposed. Some numerical result...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

Empirical mode decomposition (EMD) is proved to be an effective tool for the nonlinear and non-stationary signals. Many researchers have studied the application of EMD in a variety of fields. But few in-depth studies are related to the improvement of EMD. A new signal analysis approach based on improved EMD method is introduced in this paper. Firstly, the basic principle of EMD is introduced. T...

GIS databases often need to include maps from diverse sources. These can differ one another by many characteristics: different projections or reference systems, (slightly) different scales, etc. Theoretical and/or empirical transformations are available in literature to obtain maps in a unique system with a fixed tolerance. These transformations are nevertheless insufficient to completely remov...

This paper presents a new fast and local method of 3D surface reconstruction for scattered data. The algorithm makes use of quasiinterpolants to compute the control points from a coarse to fine hierarchy to generate a sequence of bicubic B-spline functions whose sum approaches to the desired interpolation function. Quasi-interpolants gives a procedure for deriving local spline approximation met...

High-density objects, like catheters, pacemakers or even contrast agent-filled vessels, cause characteristic streak artifacts in computed tomography (CT). Similar to metal artifacts, these streaks can be reduced by removing the dense object using segmentation and interpolation. First, we compare state-of-the-art interpolation methods like linear, spline and higher-order methods to the Healing B...

The paper is focused on the understanding of the spline function as a modern tool in data analysis. We consider three numerical methods that offer framework for the spline function’s use as the interpolation, fitting and smoothing of the data. For each of these three methods, we present the corresponding spline and the conditions required by data for using the appropriate type of spline.