Sibson’s interpolant uses Voronoi diagrams in the plane to interpolate a set of scattered data points. This paper presents an extension of this method to handle the interpolation of a set of functional curves (transfinite surface interpolation). We derive a simple formula for this new surface type which can interpolate to any number of boundary curves. In addition, a unique surface may be creat...

Smart water flooding (SWF) is a promising enhanced oil recovery (EOR) technique due to its economic advantages. For this process, wettability alteration the most accepted controlling effect that leads increased factors (RFs). The main objective of work investigate how relative permeability curves’ interpolant affects SWF mechanisms’ assessment. Wettability described by shifting these curves in ...

The Bernstein-Bézier form of a polynomial is widely used in the fields of computer aided geometric design, spline approximation theory and, more recently, for high order finite element methods for the solution of partial differential equations. However, if one wishes to compute the classical Lagrange interpolant relative to the Bernstein basis, then the resulting Bernstein-Vandermonde matrix is...

Given a B-spline M on R, s≥ 1 we consider a classical discrete quasi-interpolant Qd written in the form Qdf = ∑ i∈Zs f (i)L(· − i), where L(x) :=∑ j∈JcjM(x− j) for some finite subset J ⊂ Z and cj ∈R. This fundamental function is determined to produce a quasi-interpolation operator exact on the space of polynomials of maximal total degree included in the space spanned by the integer translates o...

In this paper, we propose to extend the hierarchical bivariateHermite Interpolant to the spherical case. Let $T$ be an arbitraryspherical triangle of the unit sphere $S$ and  let $u$ be a functiondefined over the triangle $T$. For $kin mathbb{N}$, we consider aHermite spherical Interpolant problem $H_k$ defined by some datascheme $mathcal{D}_k(u)$ and which admits a unique solution $p_k$in the ...

We describe a detailed computational procedure which, given data values at arbitrarily distributed points in the plane, determines if the data are convex and, if so, constructs a smooth convex surface that interpolates the data. The method consists of constructing a triangulation of the nodes (data abscissae) for which the triangle-based piecewise linear interpolant is convex, computing a set o...

In former articles we have given a formula for the error committed when interpolating a several times differentiable function by the sinc interpolant on a fixed finite interval. In the present workwe demonstrate the relevance of the formula through several applications: correction of the interpolant through the insertion of derivatives to increase its order of convergence, improvement of the ba...

This short note contains random thoughts about a factorization theorem for closure/interior operators on a powerset which is reminiscent to the notion of resolution for a monad/comonad. The question originated from formal topology but is interesting in itself. The result holds constructively (even if it classically has several variations); but usually not predicatively (in the sense that the in...

For n + 1 points in IR, in general position, the Kergin polynomial interpolant of C functions may be extended to an interpolant of C functions. This results in an explicit set of reduced Kergin functionals naturally stratified by their dependence on certain directional derivatives of order k, 0 ≤ k ≤ d − 1. We show that the polynomials dual to the functionals depending on derivatives of order k...