Open Access

ARTICLE

Scattered Data Interpolation Using Cubic Trigonometric Bézier Triangular Patch

Ishak Hashim¹, Nur Nabilah Che Draman², Samsul Ariffin Abdul Karim^3,*, Wee Ping Yeo⁴, Dumitru Baleanu^5,6,7
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

Received 18 December 2020; Accepted 18 January 2021; Issue published 04 June 2021

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.

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Keywords

Cubic trigonometric; Bézier triangular patches; C¹sufficient condition; scattered data interpolation

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