https://doi.org/10.1140/epjs/s11734-025-01584-1
Regular Article
A new class of cubic trigonometric zipper fractal Bézier curves with one shape parameter
1
Department of Mathematics, Indian Institute of Technology Guwahati, 781039, Guwahati, India
2
Department of Engineering Design, Indian Institute of Technology Madras, 600036, Chennai, India
Received:
26
December
2024
Accepted:
14
March
2025
Published online:
17
April
2025
A new class of cubic trigonometric zipper fractal Bézier curves is introduced using novel basis functions. These basis functions, which incorporate free parameters such as shape parameter, scaling, signature, and a base function, fulfill interval end conditions, partition of unity, non-negativity, and symmetry with certain parameter restrictions. Consequently, the resulting curves achieve endpoint interpolation, preserve the convex hull property, and maintain symmetry and geometric invariance. Utilizing this new class of curves, visually striking and captivating flower designs are created.
Mathematics Subject Classification: 28A80 / 41A05 / 42A05 / 42A10 / 42A15 / 65D17 / 68U05
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
