NEW CUBIC TIMMER TRIANGULAR PATCHES WITH C¹ AND G¹ CONTINUITY

Authors

  • Fatin Amani Mohd Ali Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia
  • Samsul Ariffin Abdul Karim Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610 Seri Iskandar, Perak Darul Ridzuan, Malaysia
  • Sarat Chandra Dass Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia
  • Vaclav Skala School of Computer Science and Engineering, University of West Bohemia, Plzen
  • Azizan Saaban School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, Kedah, Malaysia
  • Mohammad Khatim Hasan Centre for Artificial Intelligence Technology, Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
  • Ishak Hashim Centre for Modelling & Data Science, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

DOI:

https://doi.org/10.11113/jt.v81.13759

Keywords:

Cubic Timmer triangular patch, Parametric continuity, Geometric continuity, cubic Timmer curve, scattered

Abstract

In this study, a new cubic Timmer triangular patch is constructed by extending the univariate cubic Timmer basis functions. The best scheme that lies towards the control polygon is cubic Timmer curve and surface compared to the other methods. From the best of our knowledge, nobody has extended the univariate cubic Timmer basis to the bivariate triangular patch. The construction of the proposed cubic Timmer triangular patch is based on the main idea of the cubic Ball and cubic Bezier triangular patches construction. Some properties of the new cubic Timmer triangular patch are investigated. Furthermore, the composite cubic Timmer triangular patches with parametric continuity (C1) and geometric continuity (G1) are discussed. Simple error analysis between the triangular patches and one test function is provided for each continuity type. Numerical and graphical results are presented by using Mathematica and MATLAB.

Author Biographies

  • Fatin Amani Mohd Ali, Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia
    Fundamental and Applied Sciences Department
  • Samsul Ariffin Abdul Karim, Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610 Seri Iskandar, Perak Darul Ridzuan, Malaysia
    Fundamental and Applied Sciences Department
  • Sarat Chandra Dass, Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32610, Seri Iskandar, Perak Darul Ridzuan, Malaysia
    Fundamental and Applied Sciences Department
  • Vaclav Skala, School of Computer Science and Engineering, University of West Bohemia, Plzen
    School of Computer Science and Engineering
  • Azizan Saaban, School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, Kedah, Malaysia
    School of Quantitative Sciences
  • Mohammad Khatim Hasan, Centre for Artificial Intelligence Technology, Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
    Centre for Artificial Intelligence Technology, Faculty of Information Science and Technology
  • Ishak Hashim, Centre for Modelling & Data Science, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
    Centre for Modelling & Data Science, Faculty of Science & Technology

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Published

2019-09-22

Issue

Vol. 81 No. 6: November 2019

Section

Science and Engineering

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How to Cite

NEW CUBIC TIMMER TRIANGULAR PATCHES WITH C¹ AND G¹ CONTINUITY. (2019). Jurnal Teknologi (Sciences & Engineering), 81(6). https://doi.org/10.11113/jt.v81.13759