Shape-Preserving Techniques with Fractional Order C1 Linear Trigonometric Spline
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Generating a smooth curve or surface is the prime goal of interpolation. If the given interplant reflects the exact shape of the data, it would be an added advantage. In this study, a general form of Fractional Order Linear Trigonometric Spline (FOLTS) is proposed with continuity. A method for modeling imperative curves has been developed with the goal of using it in a variety of engineering, scientific, and design fields. The primary goal of this research is to combine linear trigonometric spline with Caputo derivative in order to obtain better control over the curve in each sub-interval. The curve can be manipulated locally with the help of one degree of freedom involved in the form of fractional parameters. To describe shape-preserving interpolation applications, two more parameters namely “s” and “t” have been developed. These parameters ensure that the interpolated piecewise curve is able to satisfy shape-preserving properties. The study also compares FOLTS with quadratic Lagrange and cubic spline.
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Barsky BA. A description and evaluation of various 3D models. In: Kunii TL, eds. Computer Graphics: Theory and Applications. Springer; 1983:75–95.
Hussain MZ, Sarfraz M, Shaikh TS. Shape preserving rational cubic spline for positive and convex data. Egypt Inform J. 2011;12(3):231–236. https://doi.org/10.1016/j.eij.2011.10.002
Ibraheem F, Hussain M, Hussain MZ, Bhatti AA. Positive data visualization using trigonometric function. J Appl Math. 2012;2012:e247120. https://doi.org/10.1155/2012/247120
Zhu Y, Han X, Han J. Quartic trigonometric Bézier curves and shape preserving interpolation curves. J Comput Inform Syst. (2012);8(2):905–914.
Liu S, Chen Z, Zhu Y. Rational quadratic trigonometric interpolation spline for data visualization. Math Prob Eng. 2015;2015:e983120. https://doi.org/10.1155/2015/983120
Ahlberg JH, Nilson EN, Walsh JL. The Theory of Splines and Their Applications. Vol 38. Elsevier; 2016.
Sarfraz M, Samreen S, Hussain MZ. Modeling of 2D objects with weighted-quadratic trigonometric spline. Paper presented at: 13th International Conference on Computer Graphics, Imaging and Visualization; March 29–April 1, 2016; IEEE. https://doi.org/10.1109/CGiV.2016.15
Bagley RL, Torvik PJ. Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA J. 1985;23(6):918–925. https://doi.org/10.2514/3.9007
Baillie RT. Long memory processes and fractional integration in econometrics. J Econom. 1996;73(1):5–59. https://doi.org/10.1016/0304-4076(95)01732-1
Talib I, Belgacem FBM, Asif NA, Khalil H. On mixed derivatives type high dimensions multi-term fractional partial differential equations approximate solutions. AIP Conf. Proc. 2017;1798(1):e020024. https://doi.org/10.1063/1.4972616
Kirmani S, Mariyam S, Asif NA. Fractional order C¹ cubic spline. Int J Adv Soft Comput Appl. 2018;10(3):180–189.
Singh H, Kumar D, Baleanu D. Methods of Mathematical Modelling: Fractional Differential Equations. CRC Press; 2019.
Kirmani S, Suaib NM, Riaz MB. Shape preserving fractional order KNR C1 cubic spline. Eur Phy J Plus. 2019;134(7):e319. https://doi.org/10.1140/epjp/i2019-12704-1
Kirmani SK, Riaz MB, Jarad F, Jasim HN, Enver A. Shape preserving piecewise KNR fractional order Biquadratic C2 Spline. J Math. 2021;2021:e9981153. https://doi.org/10.1155/2021/9981153
Samreen S, Sarfraz M, Jabeen N, Althobaiti S, Mohamed A. A rational quadratic trigonometric spline (RQTS) as a superior surrogate to rational cubic spline (RCS) with the purpose of designing. Appl Sci. 2022;12(8):e3992. https://doi.org/10.3390/app12083992
Samreen S, Sarfraz M, Mohamed A. A quadratic trigonometric B-Spline as an alternate to cubic B-spline. Alex Eng J. 2022;61(12):11433–11443. https://doi.org/10.1016/j.aej.2022.05.006
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