FRACTAL AND CONVEXITY ANALYSIS OF THE QUATERNARY FOUR-POINT SCHEME AND ITS APPLICATIONS

Shao-Wen Yao (), Pakeeza Ashraf (), Abdul Ghaffar (), Misbah Kousar (), Mustafa Inc and Niat Nigar ()
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Shao-Wen Yao: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China
Pakeeza Ashraf: Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan
Abdul Ghaffar: Department of Mathematics, Ghazi University, Dera Ghazi Khan 32200, Pakistan
Misbah Kousar: Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan
Mustafa Inc: Department of Mathematics, Firat University, ElaziÄŸ 23119, Turkey6Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Niat Nigar: School of Mathematics, Minhaj University Lahore, Lahore 54000, Pakistan

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-14

Abstract: The main objective of this research is to analyze some geometrical properties of a quaternary four-point interpolatory subdivision scheme (Q4-scheme) with a shape parameter and then find the precise range of the shape parameter of the Q4-scheme to generate fractal and convexity of limit curves. That allows the curve to change easily and be more flexible without altering its control points. Therefore, by taking the various values of tension parameters, the curve still preserves its characteristics and geometrical configuration. These geometric modeling examples show that our techniques can be easily performed, and they can also provide us with an alternative strong strategy for the modeling of complex figures.

Keywords: Fractal Curves; Interpolatory Subdivision Scheme; Quaternary; Algorithm; Curvature; Convexity; Computational Geometry (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400881

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