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Quartic Rational Said‐Ball‐Like Basis with Tension Shape Parameters and Its Application

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  • Yuanpeng Zhu
  • Xuli Han
  • Shengjun Liu

Abstract

Four new quartic rational Said‐Ball‐like basis functions, which include the cubic Said‐Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class of C1 continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing a C1 positivity‐ or monotonicity‐ preserving interpolation spline. In addition, we extend the quartic rational Said‐Ball‐like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said‐Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau‐type algorithm is developed. Moreover, the G1 continuous conditions are deduced for the joining of two patches.

Suggested Citation

  • Yuanpeng Zhu & Xuli Han & Shengjun Liu, 2014. "Quartic Rational Said‐Ball‐Like Basis with Tension Shape Parameters and Its Application," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:857840
    DOI: 10.1155/2014/857840
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    References listed on IDEAS

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    1. Farheen Ibraheem & Maria Hussain & Malik Zawwar Hussain & Akhlaq Ahmad Bhatti, 2012. "Positive Data Visualization Using Trigonometric Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Uzma Bashir & Jamaludin Md. Ali, 2013. "Data Visualization Using Rational Trigonometric Spline," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-10, June.
    3. Uzma Bashir & Jamaludin Md. Ali, 2013. "Data Visualization Using Rational Trigonometric Spline," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Farheen Ibraheem & Maria Hussain & Malik Zawwar Hussain & Akhlaq Ahmad Bhatti, 2012. "Positive Data Visualization Using Trigonometric Function," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, November.
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