Various Shape Functions of Magnetic Curves

Abstract

Magnetic curves are particle trajectories traced under the influence of magnetic field. It encompasses a huge family of monotonic varying curvature curves. Recently, magnetic curves with linear logarithmic curvature graph (LCG) has been derived and denoted as log-aesthetic magnetic curve (LMC), whose characteristics are similar to that of log-aesthetic curves (LAC). This paper elaborates aesthetic shapes through analyzing the particle charge function 𝑞(𝑡) of general representation of magnetic curves which dictates the monotonicity of curvature profile. This paper also proves that LMC or the generalized version of LMC is not the only representation of the family of magnetic curve with monotonic curvature profile. The investigation of the fairness of planar magnetic curves uses conventional shape interrogation methods and LCG. The result provides an insight to control the shape function 𝑞(𝑡) for the generation of fair magnetic curves and elucidate their properties for practical design purposes.