NDLI: Generalized Developable Cubic Trigonometric Bézier Surfaces

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Generalized Developable Cubic Trigonometric Bézier Surfaces

Content Provider	MDPI
Author	Ammad, Muhammad Misro, Yushalify Abbas, Muhammad Majeed, Abdul
Copyright Year	2021
Description	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 $G1$ , Farin–Boehm $G2$ , and $G2$ 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 s쳮ds and can also significantly improve the capability of solving problems in design engineering.
Starting Page	283
e-ISSN	22277390
DOI	10.3390/math9030283
Journal	Mathematics
Issue Number	3
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-01-31
Access Restriction	Open
Subject Keyword	Mathematics Manufacturing Engineering Developable Surfaces Shape Parameters Geodesic Geometric Continuity Trigonometric
Content Type	Text
Resource Type	Article

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