| Abstract: |
| A class of plane curves called the log-aesthetic curves (LAC) and their generalization used in the industrial design and the computational geometric design is considered. We give its new characterization based on the integrable deformation theory of the plane curves in the similarity geometry, together with the variational formulation by introducing the fairing energy. This implies that LAC can be regarded as the similarity geometric analogue of the celebrated Euler`s elastic curves. Based on this formulation, we propose the discrete LAC by applying the integrable discretization of the plane curve deformation in the similarity geometry. We also introduce the discrete fairing energy and formulate it by using the discrete variational principle. |
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