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

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

Journal of Mathematics, 2023, vol. 2023, 1-18

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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7457223

DOI: 10.1155/2023/7457223

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