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

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.