C1 Rational Cubic Ball Triangular Patch for Positivity Preserving Scattered Data Interpolation

Authors

  • Siti Jasmida Jamil Universiti Malaysia Perlis
  • Wan Nurhadani Wan Jaafar Institut Matematik Kejuruteraan, Universiti Malaysia Perlis, Kampus Pauh Putra, 2600 Arau, Perlis, Malaysia.
  • Shakila Saad Institut Matematik Kejuruteraan, Universiti Malaysia Perlis, Kampus Pauh Putra, 2600 Arau, Perlis, Malaysia.
  • Nooraihan Abdullah Institut Matematik Kejuruteraan, Universiti Malaysia Perlis, Kampus Pauh Putra, 2600 Arau, Perlis, Malaysia.

Abstract

This paper presents the construction of a C1 rational interpolant which is positive everywhere when given data are positive. A local positivity preserving scheme is developed using rational cubic Ball basis functions, which involves weights as free parameters. Sufficient conditions are derived on Ball ordinates in order to ensure generated surface comprising of triangular patches is always positive. Each triangular patch of the interpolating surface is represented by a convex combination of three adjoining triangular patches. Gradients at data sites are calculated and modified (if necessary). The values of weights (free parameters) may also be changed in order to generate a positive surface. The weights (free parameters) provide extra freedom to users for them to modify the shape of surface as desired. Graphical examples are illustrated.

Keywords:

Positivity preserving, Rational cubic Ball, Triangular surface, Weights (free parameters)

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Published

2023-07-31

How to Cite

Jamil, S. J., Wan Nurhadani Wan Jaafar, Shakila Saad, & Nooraihan Abdullah. (2023). C1 Rational Cubic Ball Triangular Patch for Positivity Preserving Scattered Data Interpolation. Applied Mathematics and Computational Intelligence (AMCI), 12(2), 130–150. Retrieved from https://ejournal.unimap.edu.my/index.php/amci/article/view/35

Issue

Vol. 12 No. 2 (2023): September (2023)

Section

Articles