NDLI: $G^{3}$ Shape Adjustable GHT-Bézier Developable Surfaces and Their Applications

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$G^{3}$ Shape Adjustable GHT-Bézier Developable Surfaces and Their Applications

Content Provider	MDPI
Author	BiBi, Samia Misro, Yushalify Abbas, Muhammad Majeed, Abdul Nazir, Tahir
Copyright Year	2021
Description	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 $G1$ , $G2$ (Farin-Boehm and Beta) and $G3$ 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.
Starting Page	2350
e-ISSN	22277390
DOI	10.3390/math9192350
Journal	Mathematics
Issue Number	19
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-09-22
Access Restriction	Open
Subject Keyword	Mathematics Artificial Intelligence Ght-bézier Developable Surface Shape-adjustable Property Shape Parameters Continuity of Surfaces Duality
Content Type	Text
Resource Type	Article

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