Polynomization of shape parameter α for log-aesthetic, σ- and τ -curves

Abstract

In order to further improve the expressive power of log-aesthetic curves,Tsuchie and Yoshida investigated the derivation process of log-aesthetic curves and they proposed a α-curve with variable shape parameter α. The derivation method extends the differential equation regarding curvature and curve length (arc length) that defines the log-aesthetic curve, It is a relatively complicated process deriving a new curve formula, and its intuitive meaning is not clear.In this report, we will investigate the log-aesthetic curve, its extension σ-curve and their similar curve τ-curve and propose a method to improve the ability to express curves by setting the shape parameter α to a polynomial of degree m with respect to the arc length parameter.