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

Author

Listed:
  • 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)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:924-:d:367954
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    References listed on IDEAS

    as
    1. 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).
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    Cited by:

    1. Abdul Majeed & Mehwish Naureen & Muhammad Abbas & Kenjiro T. Miura, 2022. "Construction of Cubic Trigonometric Curves with an Application of Curve Modelling," Mathematics, MDPI, vol. 10(7), pages 1-22, March.

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