IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i17p2862-d1742338.html
   My bibliography  Save this article

Interpolating Triangular Meshes Using a Non-Uniform, Non-Stationary Loop Subdivision

Author

Listed:
  • Baoxing Zhang

    (College of Statistics and Mathematics, Hebei University of Economics and Business, Shijiazhuang 050061, China)

  • Hongchan Zheng

    (School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China)

  • Huanxin Cao

    (School of Economics and Administration, Xi’an University of Technology, Xi’an 710054, China)

Abstract

This paper presents a novel non-uniform, non-stationary Loop subdivision that directly interpolates arbitrary initial triangular meshes. This subdivision is derived by assigning distinct parameters for “vertex-point” and “edge-point” generation within the stencils of a uniform, non-stationary Loop subdivision. This underlying uniform, non-stationary scheme is obtained based on a suitably chosen iterative process. Crucially, we derive the limit positions of the initial points under this non-uniform scheme and decrease the assigned parameters to a single shape parameter when interpolating the initial mesh. Compared with the existing methods interpolating the initial mesh using approximating subdivision, this new one achieves interpolation in finite steps and without any additional adjustment to the initial mesh or subdivision rules. Several numerical examples are given to show the scheme’s interpolation accuracy and shape control capabilities.

Suggested Citation

  • Baoxing Zhang & Hongchan Zheng & Huanxin Cao, 2025. "Interpolating Triangular Meshes Using a Non-Uniform, Non-Stationary Loop Subdivision," Mathematics, MDPI, vol. 13(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2862-:d:1742338
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/17/2862/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/17/2862/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:13:y:2025:i:17:p:2862-:d:1742338. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.