Abstract: This paper presents the cubic trigonometric interpolation curves with two parameters generated over the space {1, sint, cost, sin2t, sin3t, cos3t}. The new curves can not only automatically interpolate the given data points without solving equation systems, but are also C2 and adjust their shape by altering values of the two parameters. The optimal interpolation curves can be determin...

In this paper, we thoroughly study a trilinear interpolation scheme previously proposed for the Body-Centered Cubic (BCC) lattice. We think that, up to now, this technique has not received the attention that it deserves. By a frequency-domain analysis we show that it can isotropically suppress those aliasing spectra that contribute most to the postaliasing effect. Furthermore, we present an eff...

This paper presents a least square quadratic phase interpolation algorithm for sinusoidal model based music synthesis. This algorithm uses two additions with one parameter per data frame to generate the phase samples of a component sinewave. Compared with the cubic phase interpolation algorithm proposed by McAulay and Quatieri [1], the proposed algorithm is more e cient in terms of computationa...

Method for image prediction with nonlinear control lines which are derived from extracted feature points from the previously acquired imagery data based on Kriging method and morphing method is proposed. Through comparisons between the proposed method and the conventional linear interpolation and widely used Cubic Spline interpolation methods, it is found that the proposed method is superior to...

[Her13] F.Hernoux, R.Béarée, L.Gajny, E.Nyiri, J.Bancalin, O.Gibaru, Leap Motion pour la capture de mouvement 3D par spline L1. Application à la robotique. GTMG 2013, Marseille, 27-28 mars 2013 [Gib1899] J. Willard Gibbs, lettre à l’éditeur, Nature 59 (April 27, 1899) 606. [Lav00] J.E. Lavery, Univariate Cubic Lp splines and shape-preserving multiscale interpolation by univariate cubic L1 splin...

A C curve interpolation scheme for monotonic data has been developed. This scheme uses piecewise rational cubic functions. The two families of parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The monotone rational cubic spline scheme has a unique representation.

In this paper we investigate the impact of the floating-point precision and interpolation scheme on the results of direct numerical simulations (DNS) of turbulence by pseudo-spectral codes. Three different types of floating-point precision configurations show no differences in the statistical results. This implies that single precision computations allow for increased Reynolds numbers due to th...

In this paper we propose a new kind of Hermite interpolation on arbitrary domains, matching derivative data of arbitrary order on the boundary. The basic idea stems from an interpretation of mean value interpolation as the pointwise minimization of a radial energy function involving first derivatives of linear polynomials. We generalize this and minimize over derivatives of polynomials of arbit...

A trivariate Lagrange interpolation method based on C1 cubic splines is described. The splines are defined over a special refinement of the Freudenthal partition of a cube partition. The interpolating splines are uniquely determined by data values, but no derivatives are needed. The interpolation method is local and stable, provides optimal order approximation, and has linear complexity.

We derive regions for T-cubic and arc/T-cubic spirals to two-point Hermite interpolation in terms of unit tangent vectors with help of Mathematica. The use of spirals gives the designer an excellent and speedy control over the shape of curve that is produced because there are no internal curvature maxima, curvature minima, inflection points, loops and cusps in a spiral segment.