Data Visualization Using Rational Trigonometric Spline

Abstract

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using aC1piecewise rational cubic trigonometric spline with four shape parameters, are developed. Two of these shape parameters are constrained and the other two are set free to preserve the inherited shape features of the data as well as to control the shape of the curve. Numerical examples are given to illustrate the worth of the work.

Rational Cubic Spline Interpolation for Monotonic Interpolating Curve with C2 Continuity

“…From Figs. 1(d) and 1(e) the proposed 2 C rational cubic spline give smooth results compare to the works of Sarfraz et al [19] and Abbas [3]. Meanwhile from Fig.…”

“…Some examples of monotonic data includes the population at one country as well as the approximation of couples and quasi couples in statistics (Karim and Kong [13]). The usual 2 C cubic spline interpolation is very smooth but for shape preserving interpolation purpose, the cubic spline are unable to preserves the shape of the data on entire given interval resulting the interpolating curve may be oscillates on some interval. Fritsch and Carlson [8] constructed the monotonic cubic Hermite spline polynomial to preserve monotone data set.…”

“…In Sarfraz et al [19] the rational cubic spline with quadratic denominator has been used for monotonicity with 2 C continuity -without any degree freedom. Sarfraz [18] also discussed the used of rational cubic spline (cubic/cubic) for monotonicity preserving with 2 C continuity but his schemes also not received much attention since there are no degree freedom. Similarly the rational cubic spline of Gregory [9] also did not have any degree freedom i.e.…”

“…free parameters for shape modification. Abbas et al [1] discussed the monotonicity by using 2 C rational cubic spline with two free parameters. This paper is a continuation from our previous works (Karim and Kong [14]).…”

Constrained Interpolation using Rational Cubic Spline with Three Parameters

“…The sufficient conditions for constrained data interpolation are derived on one parameter, meanwhile the other two are free parameters that can be used to alter the shape of the constrained interpolating curve. The proposed scheme does not require any knots insertion or trigonometric functions as was required in the schemes of Bashir and Ali (2013), Ibraheem et al (2012) and Sarfraz et al (2015).…”