IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v378y2020ics0096300320301843.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320301843
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125215?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ze Shi & Hongyi Li & Di Zhao & Chengwei Pan, 2023. "Research on Relation Classification Tasks Based on Cybersecurity Text," Mathematics, MDPI, vol. 11(12), pages 1-16, June.
    2. 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.
    3. Li, Hongyi & Wang, Chaojie & Zhao, Di, 2020. "Preconditioning for PDE-constrained optimization with total variation regularization," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Abdul Majeed & Muhammad Abbas & Faiza Qayyum & Kenjiro T. Miura & Md Yushalify Misro & Tahir Nazir, 2020. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter," Mathematics, MDPI, vol. 8(12), pages 1-25, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s0096300320301843. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.