The Family of Log-Aesthetic Curves

Abstract

This paper clarifies the overall shapes of log-aesthetic curves. Log-aesthetic curves are curves whose logarithmic curvature graph and logarithmic torsion graph are both linear. We classify the overall shapes of log-aesthetic space curves depending on the arc length, the behavior of the tangent and binormal vectors, and the radius of curvature and radius of torsion at the bound of arc length.