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Construction of Cubic Trigonometric Curves with an Application of Curve Modelling

Author

Listed:
  • Abdul Majeed

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

  • Mehwish Naureen

    (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)

  • Kenjiro T. Miura

    (Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Shizuoka, Japan)

Abstract

This paper introduces new trigonometric basis functions (TBF) in polynomial and rational form with two shape parameters (SPs). Some classical characteristics, such as the partition of unity, positivity, symmetry, CHP, local control and invariance under affine transformation properties are proven mathematically and graphically. In addition, different continuity conditions at uniform knots (UK) are proven. Some open and closed curves from TBS and trigonometric rational B-spline (TRBS) are generated to test the applicability of the suggested technique, and the influence of the shape parameter is also noted. Furthermore, various objects, such as designing an alphabet, star, butterfly, leaf and 3D cube.

Suggested Citation

  • Abdul Majeed & Mehwish Naureen & Muhammad Abbas & Kenjiro T. Miura, 2022. "Construction of Cubic Trigonometric Curves with an Application of Curve Modelling," Mathematics, MDPI, vol. 10(7), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1087-:d:781267
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    References listed on IDEAS

    as
    1. Fenhong Li & Gang Hu & Muhammad Abbas & Kenjiro T. Miura, 2020. "The Generalized H-Bézier Model: Geometric Continuity Conditions and Applications to Curve and Surface Modeling," Mathematics, MDPI, vol. 8(6), pages 1-24, June.
    2. Abdul Majeed & Muhammad Abbas & Kenjiro T. Miura & Mohsin Kamran & Tahir Nazir, 2020. "Surface Modeling from 2D Contours with an Application to Craniofacial Fracture Construction," Mathematics, MDPI, vol. 8(8), pages 1-16, July.
    3. Majeed, Abdul & Mt Piah, Abd Rahni & Rafique, Muhammad & Abdullah, Johari Yap & Rajion, Zainul Ahmad, 2017. "NURBS curves with the application of multiple bones fracture reconstruction," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 70-84.
    4. Lanlan Yan, 2016. "Cubic Trigonometric Nonuniform Spline Curves and Surfaces," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-9, February.
    5. Van Than Dung & Tegoeh Tjahjowidodo, 2017. "A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting," PLOS ONE, Public Library of Science, vol. 12(3), pages 1-24, March.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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