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Open AccessArticle

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

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Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia
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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
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School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, Sintok, Kedah 06010, Malaysia
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Centre for Artificial Intelligence Technology, Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor 43600, Malaysia
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Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
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Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
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Department of Mathematics, Cankaya University, 06530 Ankara, Turkey
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Institute of Space Sciences, 077125 Magurele, Romania
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Authors to whom correspondence should be addressed.
Mathematics 2020, 8(2), 159; https://doi.org/10.3390/math8020159
Received: 14 November 2019 / Revised: 25 November 2019 / Accepted: 26 November 2019 / Published: 22 January 2020
(This article belongs to the Special Issue Mathematical Methods in Applied Sciences)
This paper discusses scattered data interpolation by using cubic Timmer triangular patches. In order to achieve C1 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 (R2). The higher R2 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. View Full-Text
Keywords: scattered data interpolation; cubic timmer triangular patches; cubic ball triangular patches; cubic Bezier triangular patches; convex combination scattered data interpolation; cubic timmer triangular patches; cubic ball triangular patches; cubic Bezier triangular patches; convex combination
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MDPI and ACS Style

Ali, F.A.M.; Abdul Karim, S.A.; Saaban, A.; Hasan, M.K.; Ghaffar, A.; Nisar, K.S.; Baleanu, D. Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation. Mathematics 2020, 8, 159.

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