The Generalized H-Bézier Model: Geometric Continuity Conditions and Applications to Curve and Surface Modeling

Fenhong Li, Gang Hu, Muhammad Abbas and Kenjiro T. Miura
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Fenhong Li: College of Mathematics and Computer Application, Shangluo University, Shangluo 726000, China
Gang Hu: Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, China
Muhammad Abbas: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
Kenjiro T. Miura: Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432, Japan

Mathematics, 2020, vol. 8, issue 6, 1-24

Abstract: The local controlled generalized H-Bézier model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is owed to its good geometric properties, e.g., symmetry and shape adjustable property. In this paper, some geometric continuity conditions for the generalized cubic H-Bézier model are studied for the purpose of constructing shape-controlled complex curves and surfaces in engineering. Firstly, based on the linear independence of generalized H-Bézier basis functions (GHBF), the conditions of first-order and second-order geometric continuity (namely, G 1 and G 2 continuity) between two adjacent generalized cubic H-Bézier curves are proposed. Furthermore, following analysis of the terminal properties of GHBF, the conditions of G 1 geometric continuity between two adjacent generalized H-Bézier surfaces are derived and then simplified by choosing appropriate shape parameters. Finally, two operable procedures of smooth continuity for the generalized H-Bézier model are devised. Modeling examples show that the smooth continuity technology of the generalized H-Bézier model can improve the efficiency of computer design for complex curve and surface models.

Keywords: generalized H-Bézier basis functions; generalized H-Bézier model; shape parameter; geometric continuity conditions; complex curve and surface design (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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