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Shape-adjustable generalized Bézier surfaces: Construction and it is geometric continuity conditions

Author

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  • Hu, Gang
  • Bo, Cuicui
  • Wei, Guo
  • Qin, Xinqiang

Abstract

The construction of the generalized Bézier model with shape parameters is one of the research hotspots in geometric modeling and CAGD. In this paper, a novel shape-adjustable generalized Bézier (or SG-Bézier, for short) surface of order (m, n) is introduced for the purpose to construct local and global shape controllable free-form complex surfaces. Meanwhile, some properties of SG-Bézier surfaces and the influence rules of shape parameters, as well as the constructions of special triangular and biangular SG-Bézier surfaces, are investigated. Furthermore, based on the terminal properties and linear independence of SG-Bernstein basis functions, the conditions for G1 and G2 continuity between two adjacent SG-Bézier surfaces are derived, and then simplified them by choosing appropriate shape parameters. Finally, the specific steps and applications of the smooth continuity for SG-Bézier surfaces are discussed. Modeling examples show that our methods in this paper are not only effective and can be performed easily, but also provide an alternative strategy for the construction of complex surfaces in engineering design.

Suggested Citation

  • Hu, Gang & Bo, Cuicui & Wei, Guo & Qin, Xinqiang, 2020. "Shape-adjustable generalized Bézier surfaces: Construction and it is geometric continuity conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301843
    DOI: 10.1016/j.amc.2020.125215
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    References listed on IDEAS

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    1. Hu, Gang & Qin, Xinqiang & Ji, Xiaomin & Wei, Guo & Zhang, Suxia, 2015. "The construction of λμ-B-spline curves and its application to rotational surfaces," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 194-211.
    2. Li, Hongyi & Qin, Xuyao & Zhao, Di & Chen, Jiaxin & Wang, Pidong, 2018. "An improved empirical mode decomposition method based on the cubic trigonometric B-spline interpolation algorithm," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 406-419.
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    Cited by:

    1. Fenhong Li & Gang Hu & Muhammad Abbas & Kenjiro T. Miura, 2020. "The Generalized H-Bézier Model: Geometric Continuity Conditions and Applications to Curve and Surface Modeling," Mathematics, MDPI, vol. 8(6), pages 1-24, June.
    2. Ammad, Muhammad & Misro, Md Yushalify & Ramli, Ahmad, 2022. "A novel generalized trigonometric Bézier curve: Properties, continuity conditions and applications to the curve modeling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 744-763.
    3. Xiaomin Liu & Muhammad Abbas & Gang Hu & Samia BiBi, 2021. "Degree Reduction of Q-Bézier Curves via Squirrel Search Algorithm," Mathematics, MDPI, vol. 9(18), pages 1-20, September.

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