Quasi-Log-Aesthetic Curves in Polynomial Bézier Form

Abstract

This paper presents planar quasi-log-aesthetic curves in polynomial Bézier form. Logaesthetic curves are curves that can be considered as the generalization of the Clothoid, Nielsen's spiral, logarithmic spirals and circle involute. By deriving the Taylor polynomials of log-aesthetic curves and converting the basis to Bernstein basis, we obtain quasi-log-aesthetic curves in polynomial Bézier form. We show the implementation results with logarithmic curvature graphs and a 1 G Hermite interpolation method.

Generalization of log-aesthetic curves by Hamiltonian formalism

“…which is regarded as a generalization of the one of the parabola. Yoshida et al [9,10] investigated the quasi aesthetic curves approximating the linearity of LDDC of LAC or approximating the Taylor series expansions of LAC by the polynomial forms.…”