G² Hermite Interpolation with the Log-aesthetic Curve

Abstract

Although the log-aesthetic curves are generally expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. In this paper we propose a novel method to solve the G² Hermite interpolation problem with the log-aesthetic plane curve as well as a new method to generate an S-shaped curve for G¹ Hermite interpolation. The methods proposed in the paper have been implemented as a plug-in module for a commercial CAD system and are successfully used for practical design.