IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i9p1019-d547095.html
   My bibliography  Save this article

Unified Representation of Curves and Surfaces

Author

Listed:
  • Aizeng Wang

    (School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
    State Key Laboratory of Virtual Reality Technology & System, Beijing 100191, China)

  • Gang Zhao

    (School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
    State Key Laboratory of Virtual Reality Technology & System, Beijing 100191, China)

  • Chuan He

    (School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
    State Key Laboratory of Virtual Reality Technology & System, Beijing 100191, China)

Abstract

In conventional modeling, shared control points can be employed to realize a unified representation for an object consisting of only curves or only surfaces touching one another. However, this method fails in treating the following two cases: (a) a system consisting of detached curves or surfaces; (b) a system having both curves and surfaces. The purpose of the present paper is to develop a new theoretical tool to solve such problems. By introducing the definitions of naked knot and I-mesh, the concept of I-spline is put forth, which is, in essence, an expanded B-spline or T-spline. It is verified by examples that the naked knots make I-splines flexible and effective in transforming different surfaces and/or curves into a unified one, especially in the above two cases.

Suggested Citation

  • Aizeng Wang & Gang Zhao & Chuan He, 2021. "Unified Representation of Curves and Surfaces," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1019-:d:547095
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/9/1019/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/9/1019/
    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:9:y:2021:i:9:p:1019-:d:547095. 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.