The extension of log-aesthetic planar and space curves

Abstract

Generalized Log-Aesthetic Curve (GLAC) is a high quality curve which has been enhanced from Log-Aesthetic Curve (LAC) and Generalized Cornu Spiral (GCS). LAC is synthesized from linear Logarithmic Curvature Graph (LCG), whereas GLAC can produced linear LCG gradient function. The first part of this research is dedicated to formulating offsets of LAC and the investigation of its evolutes which can be utilized to prevent cusps in LAC offset. The second part extends GLAC from planar curve to space curve and the resultant curve is denoted as Generalize Log- Aesthetic Space Curve (GLASC). GLASC is formulated by first constructing torsion profile similar to curvature profile in GLAC. It is then solved both curvature and torsion profile together with initial values in the form of Frenet-Serret frame. The final contribution of this thesis is the modification of GLAC formulation to control the curvature at the endpoints for a given length.