Explicit Continuity Conditions for G 1 Connection of S- ? Curves and Surfaces

Gang Hu, Huinan Li, Muhammad Abbas, Kenjiro T. Miura and Guoling Wei
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Gang Hu: Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, China
Huinan Li: 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 432-8011, Japan
Guoling Wei: Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, China

Mathematics, 2020, vol. 8, issue 8, 1-18

Abstract: The S- λ model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is due to its good geometric properties such as symmetry, shape adjustable property. With the aim to solve the problem that complex S- λ curves and surfaces cannot be constructed by a single curve and surface, the explicit continuity conditions for G 1 connection of S- λ curves and surfaces are investigated in this paper. On the basis of linear independence and terminal properties of S- λ basis functions, the conditions of G 1 geometric continuity between two adjacent S- λ curves and surfaces are proposed, respectively. Modeling examples imply that the continuity conditions proposed in this paper are easy and effective, which indicate that the S- λ curves and surfaces can be used as a powerful supplement of complex curves and surfaces design in computer aided design/computer aided manufacturing (CAD/CAM) system.

Keywords: S- ? basis functions; S- ? curves and surfaces; 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
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