Log-aesthetic curves as similarity geometric analogue of Euler’s elasticae. (English) Zbl 1505.65064
Summary: In this paper we consider the log-aesthetic curves and their generalization which are used in CAGD. We consider those curves under similarity geometry and characterize them as stationary integrable flow on plane curves which is governed by the Burgers equation. We propose a variational formulation of those curves whose Euler-Lagrange equation yields the stationary Burgers equation. Our result suggests that the log-aesthetic curves and their generalization can be regarded as the similarity geometric analogue of Euler’s elasticae.
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 53A04 | Curves in Euclidean and related spaces |
Keywords:
elastica; log-aesthetic curve; similarity geometry; Burgers equation; variational formulationReferences:
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