A novel class of zipper fractal Bézier curves and its graphics applications

Vijay,, M. Guru Prem Prasad and Gurunathan Saravana Kumar

Chaos, Solitons & Fractals, 2025, vol. 190, issue C

Abstract: In this article, we present a novel generalization of a Bézier curve that can be non-smooth. We name it the zipper fractal Bézier curve. This new curve is constructed using a class of zipper α-fractal polynomials corresponding to Bernstein basis polynomials. We establish sufficient conditions on the parameters to ensure these zipper α-fractal polynomials exhibit properties such as non-negativity, partition of unity, linear precision, and symmetry. Utilizing these properties, we show that the zipper fractal Bézier curve can achieve endpoint interpolation, symmetry, the convex-hull property, and geometric invariance. Using the zipper fractal Bézier curves, we create attractive deltoid-like, astroid-like, exoid-like, and six-leaf flower designs. Our findings have applications in various fields, including approximation theory, CAGD, computer graphics, art, and design.

Keywords: Fractal; Bernstein basis polynomials; Zipper; Nondifferentiability; Bézier curves; Graphical applications (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:190:y:2025:i:c:s0960077924013456

DOI: 10.1016/j.chaos.2024.115793

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