Convexity preserving C2 rational quadratic trigonometric spline

Abstract

A C 2 rational quadratic trigonometric spline interpolation has been studied using two kinds of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exists and is unique. The necessary and sufficient condition that constrain the interpolant curves to be convex in the interpolating interval or subinterval are derived. approximation properties has been discussed and confirms the expected approximation order is h 2 .

Shape Preserving Interpolation UsingC2Rational Cubic Spline

“…(vii) This paper utilized the rational cubic spline meanwhile in Dube and Tiwari [25], Pan and Wang [26], and Ibraheem et al [27] the rational trigonometric spline is used in place of standard rational cubic spline. Thus no trigonometric functions are involved.…”

Constrained Control of C^2 Rational Interpolant with Multiple Shape Parameter

“…The most commonly used splines are [see, 3,4,11] rational splines, specially the rational cubic spline with quadratic and linear denominator. Rational splines are the powerful tools for designing curves,surfaces and for geometric shapes such as controlling the curve to be in a given region.…”

Rational Trigonometric Interpolation and Constrained Control of the Interpolant Curves

“…The trigonometric B-splines were first introduced by Schoenberg [13] . A study of trigonometric splines has been made by a number of authors, [1,4,5,7,10] . It was found that problems of scattered data interpolation over spherical surfaces can be better handled in terms of accuracy, computational convenience and smoothness of the resulting surface using trigonometric splines.…”