Τ-curve: introduction of cusps to aesthetic curves. Issue 2 (2nd April 2020) - Miura, Kenjiro T; Suzuki, Sho; Usuki, Shin; Gobithaasan, R U
Abstract: Yan, Schiller, Wilensky, Carr, and Schaefer pointed out that one of the demerits of clothoid interpolation is a jumping behavior during the deformation of the curve. This phenomenon occurs because the clothoid curve cannot have a cusp, where the curve is kinked or the direction of the curve is abruptly changed. We discuss how to introduce cusps for the log-aesthetic curve including the clothoid curve and propose to use for the representation of a curve the direction angle instead of curvature and define a new curve named τ-curve, which is defined by the direction angle of the curve. Graphical Abstract: