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Generalized Developable Cubic Trigonometric Bézier Surfaces

Author

Listed:
  • Muhammad Ammad

    (School of Mathematical Sciences, Universiti Sains Malaysia, Gelugor 11800, Malaysia)

  • Md Yushalify Misro

    (School of Mathematical Sciences, Universiti Sains Malaysia, Gelugor 11800, Malaysia)

  • Muhammad Abbas

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

  • Abdul Majeed

    (Department of Mathematics, Division of Science and Technology, University of Education Lahore, Lahore 54000, Pakistan)

Abstract

This paper introduces a new approach for the fabrication of generalized developable cubic trigonometric Bézier (GDCT-Bézier) surfaces with shape parameters to address the fundamental issue of local surface shape adjustment. The GDCT-Bézier surfaces are made by means of GDCT-Bézier-basis-function-based control planes and alter their shape by modifying the shape parameter value. The GDCT-Bézier surfaces are designed by maintaining the classic Bézier surface characteristics when the shape parameters take on different values. In addition, the terms are defined for creating a geodesic interpolating surface for the GDCT-Bézier surface. The conditions appropriate and suitable for G 1 , Farin–Boehm G 2 , and G 2 Beta continuity in two adjacent GDCT-Bézier surfaces are also created. Finally, a few important aspects of the newly formed surfaces and the influence of the shape parameters are discussed. The modeling example shows that the proposed approach succeeds and can also significantly improve the capability of solving problems in design engineering.

Suggested Citation

  • Muhammad Ammad & Md Yushalify Misro & Muhammad Abbas & Abdul Majeed, 2021. "Generalized Developable Cubic Trigonometric Bézier Surfaces," Mathematics, MDPI, vol. 9(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:283-:d:490559
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    Citations

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    Cited by:

    1. Salah Eddargani & Mohammed Oraiche & Abdellah Lamnii & Mohamed Louzar, 2022. "C 2 Cubic Algebraic Hyperbolic Spline Interpolating Scheme by Means of Integral Values," Mathematics, MDPI, vol. 10(9), pages 1-13, April.
    2. Ammad, Muhammad & Misro, Md Yushalify & Ramli, Ahmad, 2022. "A novel generalized trigonometric Bézier curve: Properties, continuity conditions and applications to the curve modeling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 744-763.

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