A general formulation of Aesthetic Curves for design environment

Abstract

A planar curve called Generalized Log Aesthetic Curve segment (GLAC) has been proposed using the curve synthesis process with two types of formulation; ρ-shift and κ-shift. Both methods were carried out by extending the formulation of Generalized Cornu Spiral (GCS) in a similar manner to the Log Aesthetic Curve (LAC). The family of GLAC comprises of planar curves of high quality such as GCS, LAC, clothoid, logarithmic spiral, circle involute and etc. The GLAC segment has an additional parameter to determine its shape as compared to GCS and LAC segment, hence an extra constraint can be satisfied when shaping the GLAC segment. The final section of this paper shows some numerical examples.