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Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation

Author

Listed:
  • Fatin Amani Mohd Ali

    (Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia)

  • Samsul Ariffin Abdul Karim

    (Fundamental and Applied Sciences Department and Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia)

  • Azizan Saaban

    (School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, Sintok, Kedah 06010, Malaysia)

  • Mohammad Khatim Hasan

    (Centre for Artificial Intelligence Technology, Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor 43600, Malaysia)

  • Abdul Ghaffar

    (Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia)

  • Dumitru Baleanu

    (Department of Mathematics, Cankaya University, 06530 Ankara, Turkey
    Institute of Space Sciences, 077125 Magurele, Romania)

Abstract

This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C 1 continuity everywhere, we impose a rational corrected scheme that results from convex combination between three local schemes. The final interpolant has the form quintic numerator and quadratic denominator. We test the scheme by considering the established dataset as well as visualizing the rainfall data and digital elevation in Malaysia. We compare the performance between the proposed scheme and some well-known schemes. Numerical and graphical results are presented by using Mathematica and MATLAB. From all numerical results, the proposed scheme is better in terms of smaller root mean square error (RMSE) and higher coefficient of determination (R 2 ). The higher R 2 value indicates that the proposed scheme can reconstruct the surface with excellent fit that is in line with the standard set by Renka and Brown’s validation.

Suggested Citation

  • Fatin Amani Mohd Ali & Samsul Ariffin Abdul Karim & Azizan Saaban & Mohammad Khatim Hasan & Abdul Ghaffar & Kottakkaran Sooppy Nisar & Dumitru Baleanu, 2020. "Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation," Mathematics, MDPI, vol. 8(2), pages 1-46, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:159-:d:312217
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    References listed on IDEAS

    as
    1. Farheen Ibraheem & Malik Zawwar Hussain & Akhlaq Ahmad Bhatti, 2015. "C¹ Positive Surface over Positive Scattered Data Sites," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-22, June.
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    Cited by:

    1. Mawardi Bahri & Samsul Ariffin Abdul Karim, 2022. "Novel Uncertainty Principles Concerning Linear Canonical Wavelet Transform," Mathematics, MDPI, vol. 10(19), pages 1-17, September.
    2. Mawardi Bahri & Samsul Ariffin Abdul Karim, 2023. "Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform," Mathematics, MDPI, vol. 11(5), pages 1-15, March.

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