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A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications

Author

Listed:
  • Sidra Maqsood
  • Muhammad Abbas
  • Gang Hu
  • Ahmad Lutfi Amri Ramli
  • Kenjiro T. Miura

Abstract

Adopting a recurrence technique, generalized trigonometric basis (or GT-basis, for short) functions along with two shape parameters are formulated in this paper. These basis functions carry a lot of geometric features of classical Bernstein basis functions and maintain the shape of the curve and surface as well. The generalized trigonometric Bézier (or GT-Bézier, for short) curves and surfaces are defined on these basis functions and also analyze their geometric properties which are analogous to classical Bézier curves and surfaces. This analysis shows that the existence of shape parameters brings a convenience to adjust the shape of the curve and surface by simply modifying their values. These GT-Bézier curves meet the conditions required for parametric continuity ( , , , and ) as well as for geometric continuity ( , , and ). Furthermore, some curve and surface design applications have been discussed. The demonstrating examples clarify that the new curves and surfaces provide a flexible approach and mathematical sketch of Bézier curves and surfaces which make them a treasured way for the project of curve and surface modeling.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:4036434
    DOI: 10.1155/2020/4036434
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    Cited by:

    1. 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.
    2. Moavia Ameer & Muhammad Abbas & Kenjiro T. Miura & Abdul Majeed & Tahir Nazir, 2022. "Curve and Surface Geometric Modeling via Generalized Bézier-like Model," Mathematics, MDPI, vol. 10(7), pages 1-14, March.

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