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C¹ Positive Surface over Positive Scattered Data Sites

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  • Farheen Ibraheem
  • Malik Zawwar Hussain
  • Akhlaq Ahmad Bhatti

Abstract

The aim of this paper is to develop a local positivity preserving scheme when the data amassed from different sources is positioned at sparse points. The proposed algorithm first triangulates the irregular data using Delauny triangulation method, therewith interpolates each boundary and radial curve of the triangle by C¹ rational trigonometric cubic function. Half of the parameters in the description of the interpolant are constrained to keep up the positive shape of data while the remaining half are set free for users’ requirement. Orthogonality of trigonometric function assures much smoother surface as compared to polynomial functions. The proposed scheme can be of great use in areas of surface reconstruction and deformation, signal processing, CAD/CAM design, solving differential equations, and image restoration.

Suggested Citation

  • Farheen Ibraheem & Malik Zawwar Hussain & Akhlaq Ahmad Bhatti, 2015. "C¹ Positive Surface over Positive Scattered Data Sites," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-22, June.
    • Handle: RePEc:plo:pone00:0120658
    DOI: 10.1371/journal.pone.0120658
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    Cited by:

    1. Fatin Amani Mohd Ali & Samsul Ariffin Abdul Karim & Azizan Saaban & Mohammad Khatim Hasan & Abdul Ghaffar & Kottakkaran Sooppy Nisar & Dumitru Baleanu, 2020. "Construction of Cubic Timmer Triangular Patches and its Application in Scattered Data Interpolation," Mathematics, MDPI, vol. 8(2), pages 1-46, January.

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