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Curve and Surface Geometric Modeling via Generalized Bézier-like Model

Author

Listed:
  • Moavia Ameer

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

  • Muhammad Abbas

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

  • Kenjiro T. Miura

    (Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8561, Japan)

  • Abdul Majeed

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Tahir Nazir

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

Abstract

Generalized Bernstein-like functions (gB-like functions) with different shape parameters are used in this work. Parametric and geometric conditions in generalized form are developed. Some numerical examples of the parametric continuity (PC) and geometric continuity (GC) constraints of generalized Bézier-like curves (gB-like curves) are analyzed with graphical representation. Bézier-like symmetric rotation surfaces are constructed by gB-like curves. Vase and Capsule Taurus surfaces are modeled with the help of symmetry. The effect of shape parameters on surfaces are also analyzed. The illustrating figures reveal that the proposed curves and surfaces yield an accommodating strategy and mathematical depiction of Bézier curves and surfaces, allowing them to be a beneficial way to describe curves and surfaces.

Suggested Citation

  • Moavia Ameer & Muhammad Abbas & Kenjiro T. Miura & Abdul Majeed & Tahir Nazir, 2022. "Curve and Surface Geometric Modeling via Generalized Bézier-like Model," Mathematics, MDPI, vol. 10(7), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1045-:d:778703
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    References listed on IDEAS

    as
    1. Sidra Maqsood & Muhammad Abbas & Gang Hu & Ahmad Lutfi Amri Ramli & Kenjiro T. Miura, 2020. "A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-25, May.
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    Cited by:

    1. Andrii Nesvidomin & Serhii Pylypaka & Tetiana Volina & Irina Rybenko & Alla Rebrii, 2024. "Analytical connection between the Frenet trihedron of a direct curve and the Darboux trihedron of the same curve on the surface," Technology audit and production reserves, PC TECHNOLOGY CENTER, vol. 4(2(78)), pages 54-59, August.

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