Log-Aesthetic Flow Governed By Heat Conduction Equations

Abstract

In this research, based on the concept of the smoothing by curve shortening flow and curvature flow, we will propose log-aesthetic flow to make free-form curves “log-aesthetic.” We will discuss smoothing methods that deal with continuous curves as well as discrete ones. We have one degree of freedom α to control smoothing for log-aesthetic flow and can expect the completely smoothed shape of a given curve, which means the shape obtained by fairing, to be log-aesthetic curve. This paper shows that log-aesthetic flow is basically governed by the heat conduction equation, which has been well studied in both physics and mechanical engineering, its effects are easily inferred by the designers and it will be useful for practical aesthetic design.