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Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Author

Listed:
  • Abdul Majeed

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Muhammad Abbas

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Faiza Qayyum

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan)

  • Kenjiro T. Miura

    (Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Shizuoka 432-8011, Japan)

  • Md Yushalify Misro

    (School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia)

  • Tahir Nazir

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

Abstract

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ ∈ [ 0 , 4 ] . All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C 3 and C 5 continuities for trigonometric B-spline basis and C 3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2 D and 3 D models are also constructed using proposed curves.

Suggested Citation

  • Abdul Majeed & Muhammad Abbas & Faiza Qayyum & Kenjiro T. Miura & Md Yushalify Misro & Tahir Nazir, 2020. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter," Mathematics, MDPI, vol. 8(12), pages 1-25, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2102-:d:450222
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    References listed on IDEAS

    as
    1. Sidra Maqsood & Muhammad Abbas & Gang Hu & Ahmad Lutfi Amri Ramli & Kenjiro T. Miura, 2020. "A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-25, May.
    2. Abdul Majeed & Abd Rahni Mt Piah & R U Gobithaasan & Zainor Ridzuan Yahya, 2015. "Craniofacial Reconstruction Using Rational Cubic Ball Curves," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-14, April.
    3. Abdul Majeed & Abd Rahni Mt Piah & Zainor Ridzuan Yahya, 2016. "Surface Reconstruction from Parallel Curves with Application to Parietal Bone Fracture Reconstruction," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-16, March.
    4. Hu, Gang & Qin, Xinqiang & Ji, Xiaomin & Wei, Guo & Zhang, Suxia, 2015. "The construction of λμ-B-spline curves and its application to rotational surfaces," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 194-211.
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    Citations

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    Cited by:

    1. Abdul Majeed & Muhammad Abbas & Kenjiro T. Miura, 2022. "A Comparative Study of Different Schemes Based on Bézier-like Functions with an Application of Craniofacial Fractures Reconstruction," Mathematics, MDPI, vol. 10(8), pages 1-16, April.

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