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G 3 Shape Adjustable GHT-Bézier Developable Surfaces and Their Applications

Author

Listed:
  • Samia BiBi

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

  • Md Yushalify Misro

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

  • Muhammad Abbas

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

  • Abdul Majeed

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

  • Tahir Nazir

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

Abstract

In this article, we proposed a novel method for the construction of generalized hybrid trigonometric (GHT-Bézier) developable surfaces to tackle the issue of modeling and shape designing in engineering. The GHT-Bézier developable surface is obtained by using the duality principle between the points and planes with GHT-Bézier curve. With different shape control parameters in their domain, a class of GHT-Bézier developable surfaces can be established (such as enveloping developable GHT-Bézier surfaces, spine curve developable GHT-Bézier surfaces, geodesic interpolating surfaces for GHT-Bézier surface and developable GHT-Bézier canal surfaces), which possess many properties of GHT-Bézier surfaces. By changing the values of shape parameters the effect on the developable surface is obvious. In addition, some useful geometric properties of GHT-Bézier developable surface and the G 1 , G 2 (Farin-Boehm and Beta) and G 3 continuity conditions between any two GHT-Bézier developable surfaces are derived. Furthermore, various useful and representative numerical examples demonstrate the convenience and efficiency of the proposed method.

Suggested Citation

  • Samia BiBi & Md Yushalify Misro & Muhammad Abbas & Abdul Majeed & Tahir Nazir, 2021. "G 3 Shape Adjustable GHT-Bézier Developable Surfaces and Their Applications," Mathematics, MDPI, vol. 9(19), pages 1-23, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2350-:d:640447
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