<p>Curves are essential concepts enabling the functional and aesthetic forms in design, and the smooth, comfortable and safe trajectories in vehicle-robot systems. In recent years, the study of (log) aesthetic curves has attracted the attention of the community, due to its ubiquity in natural phenomena such as bird eggs, butterfly wings, falcon flights, as well as in man-made products such as Japanese swords and automobiles; thus new mechanisms able to encode, generate, evaluate, and deform aesthetic curves are expected to improve the throughput and the quality of the industrial design process.<br>
Basically, (log) aesthetic curves render a logarithmic curvature graph being approximated by a straight line; and polar aesthetic curves enable to model user-defined dynamics of the polar tangential angle. As such, the curvature profile becomes a by-product of the tangential angle.<br>
Aiming at applications in compounded aesthetic curves, e.g. to assemble complex silhouettes and to match a specific curvature profile, we extend the polar aesthetic curves and establish the analytical formulations to construct aesthetic curves with user-defined curvature profiles and polar tangential angle criteria. In particular, we propose the closed form analytic characterizations of polar log-aesthetic curves meeting user-defined criteria of curvature profiles and dynamics of polar tangential angles. We present numerical examples portraying the feasibility to render the logarithmic curvature graphs being represented by a straight line. Our approach enables the seamless characterization of aesthetic curves in polar coordinate system, which is potential to model aesthetic shapes with desirable aesthetic curvature profiles.</p>

On a Class of Polar Log-Aesthetic Curves

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

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