Utilizing trigonometric Bézier curves for reconstructing Arabic calligraphy: interpolating quasi-quartic and quasi-quintic curves / Noor Khairiah Razali and Athirah Hanani Mohd Fauzi

As technology continues to advance, Computer Aided Geometric Design (CAGD) is gaining popularity as a mathematical method for generating curves and surfaces. CAGD, a branch of applied mathematics, focuses on developing algorithms for creating smooth curves and surfaces efficiently. This paper explores the application of CAGD techniques to Khat Thuluth, a form of Arabic calligraphy known for its complexity and the skill required to create it. The study employs two methods of Trigonometric Bézier Curves, namely Quasi-Quartic and Quasi-Quintic, to reconstruct Arabic calligraphy. By examining how variations in shape parameters affect curve modifications, the research investigates the factors influencing the outcome. Comparison between the resulting figures and the original images, as well as the computational performance in terms of CPU time required for the entire calligraphy creation process, is conducted to evaluate the effectiveness of the two interpolation methods. The findings indicate that the Quasi-Quartic Trigonometric Bézier curve offers the most efficient reconstruction of Arabic calligraphy outlines, with a minimal CPU time of 8.453 seconds.