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Positive Data Visualization Using Trigonometric Function

Author

Listed:
  • Farheen Ibraheem
  • Maria Hussain
  • Malik Zawwar Hussain
  • Akhlaq Ahmad Bhatti

Abstract

A piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of developed interpolant is .

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:247120
    DOI: 10.1155/2012/247120
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    Cited by:

    1. Samsul Ariffin Abdul Karim & Kong Voon Pang, 2016. "Shape Preserving Interpolation Using C2 Rational Cubic Spline," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).
    2. Uzma Bashir & Jamaludin Md. Ali, 2013. "Data Visualization Using Rational Trigonometric Spline," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. 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).
    4. Jin Xie & Xiaoyan Liu, 2014. "The EH Interpolation Spline and Its Approximation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Xuli Han & Yuanpeng Zhu, 2014. "Total Positivity of the Cubic Trigonometric Bézier Basis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    6. Samsul Ariffin Abdul Karim & Kong Voon Pang & Azizan Saaban, 2015. "Positivity Preserving Interpolation Using Rational Bicubic Spline," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    7. Tyada, K.R. & Chand, A.K.B. & Sajid, M., 2021. "Shape preserving rational cubic trigonometric fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 866-891.
    8. Xinru Liu & Yuanpeng Zhu & Shengjun Liu, 2014. "Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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