Formula omitted]-Curves: Extended log-aesthetic curves with variable shape parameter

Abstract

This paper proposes a novel curve called the α-curve, which is specified by a variable shape parameter α and can be applied in curve reconstruction involving curve fairing, fitting, and segmentation. In contrast to classical log-aesthetic curves in which α is constant, this study contributes a novel formulation of α that varies monotonically within a specified segment. By introducing the variable α, the logarithmic curvature graph (LCG) becomes piecewise linear and parabolic, or any other function if necessary. Consequently, in comparison to conventional log-aesthetic curves that have limited field usage based on their rigidity, α-curves have various LCGs and flexible representations, thereby opening up many practical applications. Experimental results and comparative studies on curves created by CAD experts in the automotive industry demonstrate the theoretical and practical validity of α-curves.