Most operational models in atmospheric physics, meteorology and climatology nowadays adopt spherical geodesic grids and require “ad hoc” developed interpolation procedures. The author does a comparison between chosen representatives of linear, distance based and cubic interpolation schemes outlining their advantages and drawbacks in this specific application field. Numerical experiments on a st...

Image scaling is a frequent operation in video processing for optical metrology. In the paper, results of comparative study of computational complexity of different algorithms for scaling digital images with arbitrary scaling factors are presented and discussed. The following algorithms were compared: different types of spatial domain processing algorithms (linear, cubic, cubic spline interpola...

To improve the accuracy of digital image edge detection, an ENO nonlinear fourth-order interpolation based subpixel edge detection algorithm was proposed in this paper. A stencil was constructed through classical Canny operator, followed by processing gray images to generate gradient images. ENO nonlinear fourth-order interpolation was applied in the gradient direction of target edges, and then...

In the context of radial basis function interpolation, the construction of native spaces and the techniques for proving error bounds deserve some further clari cation and improvement. This can be described by applying the general theory to the special case of cubic splines. It shows the prevailing gaps in the general theory and yields a simple approach to local error bounds for cubic spline int...

This paper presents a simple and fast recurrence equation-based method for solving the cubic spline interpolation problem. The computational complexity of the method is O(n), where n is the number of measurements. The recurrence equation-based method is illustrated by an example that estimates the movement of a moving object. The paper also describes a MATLAB implementation of the new method an...

The aim of this paper is to test different types of spatial interpolation for the materialpoint method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical cantilevered beam problem. As shown in the paper, the use of negative shape functions is not consisten...

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...

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...

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...