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Exploring q-Bernstein-Bézier surfaces in Minkowski space: Analysis, modeling, and applications

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  • Sadia Bashir
  • Daud Ahmad
  • Ghada Ali

Abstract

In this paper, we examine q-Bernstein-Bézier surfaces in Minkowski space-R 1 3 with q as the shape parameter. These surfaces, a generalization of Bézier surfaces, have applications in mathematics, computer-aided geometric design, and computer graphics for the surface formation and modeling. We analyze the timelike and spacelike cases of q-Bernstein-Bézier surfaces using known boundary control points. The mean curvature and Gaussian curvature of these q-Bernstein-Bézier surfaces are computed by finding the respective fundamental coefficients. We also investigate the shape operator dependency for timelike and spacelike q-Bernstein-Bézier surfaces in Minkowski space-R 1 3, and provide biquadratic and bicubic q-Bernstein-Bézier surfaces as illustrative examples for different values of the shape controlling parameter q.

Suggested Citation

  • Sadia Bashir & Daud Ahmad & Ghada Ali, 2024. "Exploring q-Bernstein-Bézier surfaces in Minkowski space: Analysis, modeling, and applications," PLOS ONE, Public Library of Science, vol. 19(5), pages 1-26, May.
    • Handle: RePEc:plo:pone00:0299892
    DOI: 10.1371/journal.pone.0299892
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    References listed on IDEAS

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    1. Daud Ahmad & Bilal Masud, 2013. "A Coons Patch Spanning a Finite Number of Curves Tested for Variationally Minimizing Its Area," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-15, March.
    2. Daud Ahmad & Bilal Masud, 2013. "A Coons Patch Spanning a Finite Number of Curves Tested for Variationally Minimizing Its Area," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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