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

Author

Listed:
  • 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
    Department of Medical Research, China Medical University, Taichung 40402, Taiwan)

  • Tahir Nazir

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

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.

Suggested Citation

  • Moavia Ameer & Muhammad Abbas & Thabet Abdeljawad & Tahir Nazir, 2022. "A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters," Mathematics, MDPI, vol. 10(3), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:376-:d:734345
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