IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2148-d628590.html
   My bibliography  Save this article

Planar Typical Bézier Curves with a Single Curvature Extremum

Author

Listed:
  • Chuan He

    (School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China
    State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China
    State Key Laboratory of Virtual Reality Technology & Systems, Beihang University, Beijing 100191, China)

  • Gang Zhao

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

  • Aizeng Wang

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

  • Shaolin Li

    (State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China)

  • Zhanchuan Cai

    (Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China)

Abstract

This paper focuses on planar typical Bézier curves with a single curvature extremum, which is a supplement of typical curves with monotonic curvature by Y. Mineur et al. We have proven that the typical curve has at most one curvature extremum and given a fast calculation formula of the parameter at the curvature extremum. This will allow designers to execute a subdivision at the curvature extremum to obtain two pieces of typical curves with monotonic curvature. In addition, we put forward a sufficient condition for typical curve solutions under arbitrary degrees for the G1 interpolation problem. Some numerical experiments are provided to demonstrate the effectiveness and efficiency of our approach.

Suggested Citation

  • Chuan He & Gang Zhao & Aizeng Wang & Shaolin Li & Zhanchuan Cai, 2021. "Planar Typical Bézier Curves with a Single Curvature Extremum," Mathematics, MDPI, vol. 9(17), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2148-:d:628590
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2148/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/17/2148/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    typical Bézier curves; monotonic curvature; curvature extremum; G1 interpolation;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets

    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:17:p:2148-:d:628590. 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.