IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i10p2369-d1151394.html
   My bibliography  Save this article

Construction of Local-Shape-Controlled Quartic Generalized Said-Ball Model

Author

Listed:
  • Jiaoyue Zheng

    (School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China)

  • Xiaomin Ji

    (School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China)

  • Zhaozhao Ma

    (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China)

  • Gang Hu

    (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China)

Abstract

Said-Ball curves and surfaces are extensively applied in the realm of geometric modeling. Their appearance is only decided by the control points, which produces a great deal of inconvenience for the shape design of sophisticated products. To overcome this defect, we construct a novel kind of quartic generalized Said-Ball (QGS-Ball, for short) curves and surfaces, which contain multiple shape parameters, and the global and local shape can be easily modified via shape parameters. The specific research contents are as follows: Firstly, the QGS-Ball basis functions carrying multiple shape parameters are defined, and the correlative properties are proved. Secondly, the QGS-Ball curve is proposed according to the QGS-Ball basis functions, and the effect of shape parameters on the curve is discussed. Thirdly, in view of the constructed QGS-Ball curve, we further propose the combined quartic generalized Said-Ball (CQGS-Ball, for short) curves, and deduce the conditions of first-order and second-order geometric continuity (namely, G 1 and G 2 continuity). Finally, the QGS-Ball surface is defined by tensor product method, and the influence of shape parameters on the surface is analyzed. The main contribution of this article is to construct the QGS-Ball curve model, and deduce the G 1 and G 2 geometric joining conditions of QGS-Ball curves. Combined with some modeling examples, it further illustrates that the QGS-Ball curve as a new geometric model provides a powerful supplement for the geometric design of sophisticated form in computer-aided design (CAD) and computer-aided manufacturing (CAM) systems.

Suggested Citation

  • Jiaoyue Zheng & Xiaomin Ji & Zhaozhao Ma & Gang Hu, 2023. "Construction of Local-Shape-Controlled Quartic Generalized Said-Ball Model," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2369-:d:1151394
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/10/2369/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/10/2369/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fateme Ghomanjani & Samad Noeiaghdam, 2021. "Application of Said Ball Curve for Solving Fractional Differential-Algebraic Equations," Mathematics, MDPI, vol. 9(16), pages 1-10, August.
    Full references (including those not matched with items on IDEAS)

    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.

      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:gam:jmathe:v:11:y:2023:i:10:p:2369-:d:1151394. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      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.