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The Quasi‐Cubic Trigonometric Cardinal Spline With Local Shape Adjustability

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  • Juncheng Li
  • Shanjun Liu
  • Chengzhi Liu

Abstract

The cubic Cardinal spline curve is a fundamental tool in the field of interpolation curve design. However, the cubic Cardinal spline curve cannot adjust its shape locally through the free parameters, and it struggles to accurately represent common engineering curves such as elliptical arcs, circular arcs, and parabolic arcs. To overcome these limitations, a novel quasi‐cubic trigonometric Cardinal spline curve is developed. This new spline curve retains the core advantages of the cubic Cardinal spline curve while introducing significant enhancements. It incorporates free parameters that enable local shape adjustment and is capable of accurately representing elliptical arcs, circular arcs, and parabolic arcs. Additionally, the cubic Cardinal spline surface is introduced, and the schemes for creating fair quasi‐cubic trigonometric Cardinal spline curve and surface are provided.

Suggested Citation

  • Juncheng Li & Shanjun Liu & Chengzhi Liu, 2025. "The Quasi‐Cubic Trigonometric Cardinal Spline With Local Shape Adjustability," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:1325466
    DOI: 10.1155/jom/1325466
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    References listed on IDEAS

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    1. Sidra Maqsood & Muhammad Abbas & Gang Hu & Ahmad Lutfi Amri Ramli & Kenjiro T. Miura, 2020. "A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-25, May.
    2. Salma Naseer & Muhammad Abbas & Homan Emadifar & Samia Bi Bi & Tahir Nazir & Zaheer Hussain Shah & Muhammad Aslam, 2021. "A Class of Sextic Trigonometric Bézier Curve with Two Shape Parameters," Journal of Mathematics, Hindawi, vol. 2021, pages 1-16, June.
    3. Lanlan Yan, 2016. "Cubic Trigonometric Nonuniform Spline Curves and Surfaces," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-9, February.
    4. Han, Xuli, 2015. "Piecewise trigonometric Hermite interpolation," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 616-627.
    5. Moavia Ameer & Muhammad Abbas & Thabet Abdeljawad & Tahir Nazir, 2022. "A Novel Generalization of Bézier-like Curves and Surfaces with Shape Parameters," Mathematics, MDPI, vol. 10(3), pages 1-19, January.
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    Cited by:

    1. Li, Juncheng & Liu, Chengzhi, 2026. "A quintic polynomial spline with local shape parameters unifying approximation and interpolation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 582-590.

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