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

Samia BiBi, Md Yushalify Misro, Muhammad Abbas, Abdul Majeed and Tahir Nazir
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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

Mathematics, 2021, vol. 9, issue 19, 1-23

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.

Keywords: GHT-Bézier developable surface; shape-adjustable property; shape parameters; continuity of surfaces; duality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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