Generalization of log-aesthetic curves by Hamiltonian formalism

摘要

In the field of industrial shape design, the plane curves which have radii of curvature proportional to the power of linear functions of their arc-length parameters are called the log-aesthetic curves (LAC) and have been investigated. However, the well-used curves, for example, the parabolic arcs and the typical curves of Mineur et al. are not contained in the family of LACs. In this letter we generalize LAC by the Hamiltonian formalism. This extended family of curves contains some well-known plane curves in classical differential geometry.