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ARTICLE

# Scattered Data Interpolation Using Cubic Trigonometric Bézier Triangular Patch

Ishak Hashim1, Nur Nabilah Che Draman2, Samsul Ariffin Abdul Karim3,*, Wee Ping Yeo4, Dumitru Baleanu5,6,7

1 Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM, Bangi, 43600, Selangor Darul Ehsan, Malaysia
2 Department of Fundamental and Applied Sciences, Universiti Teknologi PETRONAS, Seri Iskandar, 32610, Perak Darul Ridzuan, Malaysia
3 Department of Fundamental and Applied Sciences and Centre for Systems Engineering (CSE), Institute of Autonoumous System Universiti Teknologi PETRONAS, Seri Iskandar, 32610, Perak Darul Ridzuan, Malaysia
4 Faculty of Science, Universiti Brunei Darussalam, Bandar Seri Begawan, BE1410, Brunei Darussalam
5 Department of Mathematics, Cankaya University, Ankara, Turkey
6 Institute of Space Sciences, Magurele-Bucharest, Romania
7 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

* Corresponding Author: Samsul Ariffin Abdul Karim. Email:

Computers, Materials & Continua 2021, 69(1), 221-236. https://doi.org/10.32604/cmc.2021.016006

## Abstract

This paper discusses scattered data interpolation using cubic trigonometric Bézier triangular patches with continuity everywhere. We derive the condition on each adjacent triangle. On each triangular patch, we employ convex combination method between three local schemes. The final interpolant with the rational corrected scheme is suitable for regular and irregular scattered data sets. We tested the proposed scheme with 36,65, and 100 data points for some well-known test functions. The scheme is also applied to interpolate the data for the electric potential. We compared the performance between our proposed method and existing scattered data interpolation schemes such as Powell–Sabin (PS) and Clough–Tocher (CT) by measuring the maximum error, root mean square error (RMSE) and coefficient of determination (). From the results obtained, our proposed method is competent with cubic Bézier, cubic Ball, PS and CT triangles splitting schemes to interpolate scattered data surface. This is very significant since PS and CT requires that each triangle be splitting into several micro triangles.

## Keywords

APA Style
Hashim, I., Draman, N.N.C., Karim, S.A.A., Yeo, W.P., Baleanu, D. (2021). Scattered data interpolation using cubic trigonometric bézier triangular patch. Computers, Materials & Continua, 69(1), 221-236. https://doi.org/10.32604/cmc.2021.016006
Vancouver Style
Hashim I, Draman NNC, Karim SAA, Yeo WP, Baleanu D. Scattered data interpolation using cubic trigonometric bézier triangular patch. Comput Mater Contin. 2021;69(1):221-236 https://doi.org/10.32604/cmc.2021.016006
IEEE Style
I. Hashim, N.N.C. Draman, S.A.A. Karim, W.P. Yeo, and D. Baleanu "Scattered Data Interpolation Using Cubic Trigonometric Bézier Triangular Patch," Comput. Mater. Contin., vol. 69, no. 1, pp. 221-236. 2021. https://doi.org/10.32604/cmc.2021.016006

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