The existence of inflection points for generalized log-aesthetic curves satisfying G1 data

• Main Authors: Karpagavalli, R., Gobithaasan, R. U., Miura, K. T., Shanmugavel, Madhavan
• Format: Conference or Workshop Item
• Language: English
• Published: 2015
• Subjects: QA Mathematics
• Online Access: http://repo.uum.edu.my/16795/1/1.pdf; http://repo.uum.edu.my/16795/; http://doi.org/10.1063/1.4937016
• Institution: Universiti Utara Malaysia

Log-Aesthetic (LA) curves have been implemented in a CAD/CAM system for various design feats.LA curves possess linear Logarithmic Curvature Graph (LCG) with gradient (shape parameter) denoted as α.In 2009, a generalized form of LA curves called Generalized Log-Aesthetic Curves (GLAC) has been proposed which has an extra shape parameter as ν compared to LA curves.Recently, G1 continuous GLAC algorithm has been proposed which utilizes the extra shape parameter using four control points.This paper discusses on the existence of inflection points in a GLAC segment satisfying G1 Hermite data and the effect of inflection point on convex hull property.It is found that the existence of inflection point can be avoided by manipulating the value of α.Numerical experiments show that the increase of α may remove the inflection point (if any) in a GLAC segment.