Generalization of log-aesthetic curves by Hamiltonian formalism. (English) Zbl 1426.53007
Summary: 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 Y. Mineur et al. [Comput. Aided Geom. Des. 15, No. 9, 879–891 (1998; Zbl 0910.68211)] 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.
MSC:
| 53A05 | Surfaces in Euclidean and related spaces |
Keywords:
log-aesthetic curve; similarity curvature; Riccati equation; Hamiltonian system; quasi aesthetic curveCitations:
Zbl 0910.68211References:
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