Generation of fractal curves using new binary 8-point interpolatory subdivision scheme

Autor: Abdul Ghaffar, Sadia Javed, Ghulam Mustafa, Ali Akgül, Murad Khan Hassani
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Applied Mathematics in Science and Engineering, Vol 32, Iss 1 (2024)
Druh dokumentu: article
ISSN: 27690911
2769-0911
DOI: 10.1080/27690911.2024.2367718
Popis: The subdivision scheme is a valuable tool for designing shapes and representing geometry in computer-aided geometric design. It has excellent geometric properties, such as fractals and adjustable shape. In this research paper, we explore the generation of fractal curves using a novel binary 8-point interpolatory subdivision scheme with two parameters. We analyse different properties of the proposed scheme, including convergence, special cases, and fractals. Additionally, we demonstrate through various examples the relationship between the shape parameters and the fractal behaviour of the resulting curve. Our research also identifies a specific range of shape parameters that can effectively produce fractal curves. The findings of this study provide a fast and efficient method for generating fractals, as demonstrated by numerous examples. Modelling examples show that the 8-point interpolatory scheme can enhance the efficiency of computer design for complex models.
Databáze: Directory of Open Access Journals
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