Interpolation is a form of function approximation in which the approximating function (interpolant) and the underlying function must agree at a finite number of points. In some cases additional restrictions may be imposed on the interpolant. For example its first derivative evaluated at a finite number of points may have to agree with that of the underlying function. Other examples include addi...

Visualization depends among other things on the interpolant used in generating images. One way to assess this is to construct case tables for Marching Cubes that represent the chosen interpolant accuracy. Instead, we show how to construct the interpolants induced by Marching Cases for comparison and assessment, how to extend this approach to Marching Squares, Cubes and Hypercubes, and how to co...

4. Hermite Interpolants . . , . . . . . . . . . . . . . 104 4.1. The Co nine parameter interpolant ...... 104 4.2. C’ quintic interpolants .............. 104 4.3. The general case ................... 106 5. Split Triangle Interpolants . . . . . . . . . 107 5.1. The C’ Clough-Tocher interpolant . . _ . . 108 5.2. Limitations of the Clough-Tocher split . 110 5.3. The C’ Powell-Sabin interpolants ...

We give a method of constructing an interpolant for linear equality, and inequality constraints over the rational numbers. Our method is based on efficient rewriting techniques, and does not require the use of combination methods. The interpolant is constructed in such a way that it reflects the structure of the rewrite proof.

We introduce a general definition of refinable Hermite interpolants and investigate their general properties. We also study a notion of symmetry of these refinable interpolants. Results and ideas from the extensive theory of general refinement equations are applied to obtain results on refinable Hermite interpolants. The theory developed here is constructive and yields an easyto-use constructio...

I present a new syntactical method for proving the Interpolation Theorem for the implicational fragment of intuitionistic logic and its substructural subsystems. This method, like Prawitz’s, works on natural deductions rather than sequent derivations, and, unlike existing methods, always finds a ‘strongest’ interpolant under a certain restricted but reasonable notion of what counts as an ‘inter...

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 ...

In this paper we prove that there exists a unique positive symmetrical univariate B-spline with minimal support. It is obtained as linear combination of a minimal number of successive classical B-splines with multiple knots in the space, S d , of cardinal polynomial splines of class C and degree d. Next, we show that the approximation order in the space generated by the integer translates of th...

Rational functions have deep system-theoretic significance. They represent the natural way of modeling linear dynamical systems in frequency (Laplace) domain. Using rational functions, goal this paper to compute models that match (interpolate) given data sets measurements. In paper, authors show using special orthonormal systems, Malmquist-Takenaka it is possible write interpolant $r_{(n, m)}$,...