A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters

Moavia Ameer, Muhammad Abbas, Thabet Abdeljawad and Tahir Nazir
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Moavia Ameer: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Muhammad Abbas: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Thabet Abdeljawad: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Tahir Nazir: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

Mathematics, 2022, vol. 10, issue 3, 1-19

Abstract: Bézier curves and surfaces with shape parameters have received more attention in the field of engineering and technology in recent years because of their useful geometric properties as compared to classical Bézier curves, as well as traditional Bernstein basis functions. In this study, the generalized Bézier-like curves (gBC) are constructed based on new generalized Bernstein-like basis functions (gBBF) with two shape parameters. The geometric properties of both gBBF and gBC are studied, and it is found that they are similar to the classical Bernstein basis and Bézier curve, respectively. Some free form curves can be modeled using the proposed gBC and surfaces as the applications.

Keywords: generalized Bernstein-like basis functions; generalized Bézier-like curves; surfaces; shape parameters; classical Bézier curves; geometric properties (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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