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The Approximation of Generalized Log-Aesthetic Curves with G2 Cubic Trigonometric Bézier Function

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  • Diya’ J. Albayari
  • R. U. Gobithaasan
  • Kenjiro T. Miura
  • Kenan Yildirim

Abstract

One of the requirements of curves in computer-aided design (CAD) is a curve with monotonic curvature profiles. Generalized log-aesthetic curves (GLACs) comprise a family of aesthetic curves which possesses a monotonic curvature profile. However, we cannot directly implement GLAC in CAD systems since it is in the form of a transcendental form. In this paper, we used cubic trigonometric Bézier (T-Bézier) curves with two shape parameters to approximate GLAC with G2 continuity. The final approximation formula inherits the shape parameters of GLAC whereas T-Béziers’ shape parameters are utilized to satisfy G2 constraints. Numerical results indicate that the proposed algorithm is capable of approximating GLAC within the given tolerance in (at least) two iterations.

Suggested Citation

  • Diya’ J. Albayari & R. U. Gobithaasan & Kenjiro T. Miura & Kenan Yildirim, 2023. "The Approximation of Generalized Log-Aesthetic Curves with G2 Cubic Trigonometric Bézier Function," Journal of Mathematics, Hindawi, vol. 2023, pages 1-18, September.
    • Handle: RePEc:hin:jjmath:7457223
    DOI: 10.1155/2023/7457223
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