This paper proves convergence rates for local scattered data interpolation by polyharmonic splines. To this end, it is shown that the Lagrange basis functions of polyharmonic spline interpolation are invariant under uniform scalings. Consequences of this important result for the numerical stability of the local interpolation scheme are discussed. A stable algorithm for the evaluation of polyhar...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...

Ultrasound Diffraction Tomography (UDT) is an important alternative to conventional B-mode imaging. Generally, in diffraction tomography, the most universal available computational strategies for reconstructing the object from its projections are interpolation in the frequency domain and interpolation in the space domain. They are analogous to the direct Fourier inversion and backprojection alg...

In this paper we present a NURBS version of the rational interpolating spline with tension introduced in [2], and we extend our proposal to the rectangular topology case. In particular we present some rational interpolating techniques that enable us to reconstruct shape-preserving bivariate NURBS and allow us to interactively modify the resulting surface by a set of tension parameters.

In this paper, we present a novel and robust spline interpolation algorithm given a noisy symmetric positive definite (SPD) tensor field. We construct a B-spline surface using the Riemannian metric of the manifold of SPD tensors. Each point of this surface corresponds to a diffusion tensor. We develop an algorithm for fitting such a Tensor Spline to a given tensor field and also an algorithm fo...

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...

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

Based on analysis of basic cubic spline interpolation, the clamped cubic spline interpolation is generalized in this paper. The methods are presented on the condition that the first derivative and second derivative of arbitrary node are given. The Clamped spline and Curvature-adjusted cubic spline are also generalized. The methods are presented on the condition that the first derivatives of arb...

Even though isogeometric analysis has a clear advantage regarding the number of degrees of freedom needed to achieve a certain level of accuracy, the time needed for matrix assembly (by means of numerical integration of stiffness or mass matrix entries) constitutes a severe bottleneck in the process. In order to overcome this difficulty, we propose the new approach of Integration by Interpolati...

The interpolation algorithm plays an essential role in the digital image correlation (DIC) technique for shape, deformation, and motion measurements with subpixel accuracies. At the present, little effort has been made to improve the interpolation methods used in DIC. In this Letter, a family of recursive interpolation schemes based on B-spline representation and its inverse gradient weighting ...