Log-aesthetic space curve segments

Abstract

For designing aesthetic surfaces, such as the car bodies, it is very important to use aesthetic curves as characteristic lines. In such curves, the curvature should be monotonically varying, since it dominates the distortion of reflected images on curved surfaces. In this paper, we present an interactive control method of log-aesthetic space curves. We define log-aesthetic space curves to be curves whose logarithmic curvature and torsion graphs are both linear. The linearity of these graphs constrains that the curvature and torsion are monotonically varying. We clarify the characteristics of log-aesthetic space curves and identify their family. Moreover, we present a novel method for drawing a log-aesthetic space curve segment by specifying two endpoints, their tangents, the slopes, α and β, of straight lines of the logarithmic curvature and torsion graphs, and the torsion parameter Ω. Our implementation shows that log-aesthetic curve segments can be controlled fully interactively.