Fitting Arabic Letter "Baa" Using Bézier-Like Curves with Two Shape-Parameters Basis

Abstract

Arabic font modeling is considered one of the most challenging problems in computational geometry due to the cursive and highly flexible structure of Arabic characters. In this paper, a new trigonometric–exponential basis with two shape parameters is proposed for constructing Bézier-like curves and applying them to Arabic font fitting. The proposed basis preserves the fundamental geometric properties of classical Bernstein basis functions, including non-negativity, partition of unity, endpoint interpolation, and convex hull property, while introducing additional flexibility through adjustable shape parameters. The influence of the parameters on the geometric behavior of the curve is analyzed. A least-squares fitting method is employed to approximate contour data extracted from the Arabic letter “Baa”.

Numerical experiments demonstrate that the proposed Bézier-like curve gives more accurate fitting results than the classical cubic Bézier curve in several cases, particularly when suitable values of the shape parameters are selected. The proposed approach also improves local shape control without increasing the degree of the curve or the number of control points. The results indicate that the introduced basis is effective for digital typography, Arabic calligraphy reconstruction, geometric modeling, and computer-aided font design.