IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3473-d1215031.html
   My bibliography  Save this article

A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

Author

Listed:
  • Baotao Chi

    (School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China
    Shandong Luoxiang Automobile Manufacturing Postdoctoral Research Institute, Linyi 276211, China)

  • Shengmin Bai

    (School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China)

  • Qianjian Guo

    (School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China)

  • Yaoming Zhang

    (School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China)

  • Wei Yuan

    (School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China)

  • Can Li

    (Institute of Advanced Ocean Study, Ocean University of China, Qingdao 266100, China)

Abstract

The present paper provides a new definition of the dual interpolation curve in a geometric-intuitive way based on adaptive curve refinement techniques. The dual interpolation curve is an implementation of the interpolatory subdivision scheme for curve modeling, which comprises polynomial segments of different degrees. Dual interpolation curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, and continuous and discontinuous boundary representation. In addition, the dual interpolation curve is mainly applied to solve the difficult geometry defeaturing problems for curve modeling in existing computer-aided technology. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual interpolation curve is flexible and convenient for characterizing a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of characterizing the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.

Suggested Citation

  • Baotao Chi & Shengmin Bai & Qianjian Guo & Yaoming Zhang & Wei Yuan & Can Li, 2023. "A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing," Mathematics, MDPI, vol. 11(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3473-:d:1215031
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3473/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3473/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Qiang Wang & Pyeoungkee Kim & Wenzhen Qu, 2022. "A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    2. Li, Xin & Chang, Yubo, 2018. "Non-uniform interpolatory subdivision surface," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 239-253.
    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.
    1. Samir, Chafik & Huang, Wen, 2021. "Coordinate descent optimization for one-to-one correspondence and supervised classification of 3D shapes," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    2. Kaijun Peng & Jieqing Tan & Li Zhang, 2023. "Polynomial-Based Non-Uniform Ternary Interpolation Surface Subdivision on Quadrilateral Mesh," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    3. Samir, Chafik & Adouani, Ines, 2019. "C1 interpolating Bézier path on Riemannian manifolds, with applications to 3D shape space," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 371-384.
    4. Mustafa, Ghulam & Hameed, Rabia, 2019. "Families of non-linear subdivision schemes for scattered data fitting and their non-tensor product extensions," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 214-240.

    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:16:p:3473-:d:1215031. 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.