The cubic spline interpolation method, the Runge–Kutta method, and the Newton–Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Fortran and some exam...

This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then se...

We extend the classical Budan-Fourier theorem to Hermite-Birkhoff splines, that is splines whose knots are determined by a finite incidence matrix. This is then applied to problems of interpolation by Hermite-Birkhoff splines, where the nodes of interpolation are also determined by a finite incidence matrix. For specified knots and nodes in a finite interval, conditions are examined under which...

In this paper, we purposed a new method in modeling the uncertainty data based on the theory of fuzzy sets and the interpolation B-spline model curve. The uncertainty data firstly defined by using fuzzy number concept and fuzzy relation by defined them in real data form. The existed coefficient control of interpolation B-spline basis function is substituted with the fuzzy data points(FDPs) whic...

Crown simulation based on basis spline (b-spline) interpolation is a compatible method to simulate tree polymorphism at present. However, there are two problems when it simulates the crown: first problem that derivative value top point needs be given manually, and second type of collected equidistantly. To solve above realize convenient accurate simulation, this study took Chinese fir as object...

The interpolation of a sequence of points is an important task in Engineering. In this work, three different interpolation methods are studied and expanded. The first method is the conventional interpolation Spline. The second method is a subdivision based geometric algorithm. The third method interpolates a given set of points with additional point normal constraints. The last two methods were...

B-splines provide an accurate and efficient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined proble...

We present a Hermite interpolation problem via splines of odd-degree which, to the best knowledge of the authors, has not been considered in the literature on interpolation via odd-degree splines. In this new interpolation problem, we conjecture that the interpolation error is bounded in the supremum norm independently of the locations of the knots. Given an integer k ≥ 3, our spline interpolan...

The aim of this paper is to present a general approach to the problem of shape preserving interpolation. The problem of convexity preserving interpolation using C Hermite splines with one free generating function is considered.