A new measure of fairness for curves

Abstract

This paper proposes a novel measure based on curvature variation to evaluate the fairness of curves. It is demonstrated that, in the simplest case, controlling the curvature using the proposed measure results in the log-aesthetic curve (LAC). In other words, by utilizing the proposed measure as a novel shape parameter, a unified framework can be established for aesthetic curves that accommodates a broader range of curvature variations, encompassing the LAC as a special case. Several examples are presented to illustrate curve evaluation using the proposed measure, along with its application to the approximation of aesthetic curves. The findings of this study offer a new perspective for understanding and evaluating the geometric properties of curves, with potential applications in curve design, analysis, and fairing.