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Minimum variation log-aesthetic surfaces and their applications for smoothing free-form shapes
Suzuki, Sho,Gobithaasan, R.U.,Salvi, Peter,Usuki, Shin,Miura, Kenjiro T. Society for Computational Design and Engineering 2018 Journal of computational design and engineering Vol.5 No.2
The log-aesthetic curve, which includes the logarithmic (equiangular) spiral, clothoid, and involute of a circle, achieves a control over curvature distribution by defining its shape as an integral form of its curvature and they are expected to be utilized for the field of design. However, it is very difficult to extend it to surfaces and the existing formulations have some problems that they cannot use arbitrary boundary curves. In this paper, we propose ''minimum variation log-aesthetic surface" as a new formulation for the log-aesthetic surface. Based on variational principle our method can generate surfaces by minimizing the objective function newly proposed in this paper for given arbitrary boundary curves.
τ-curve: introduction of cusps to aesthetic curves
Kenjiro T. Miura,Sho Suzuki,Shin Usuki,R.U. Gobithaasan 한국CDE학회 2020 Journal of computational design and engineering Vol.7 No.2
Yan, Schiller, Wilensky, Carr, and Schaefer pointed out that one of the demerits of clothoid interpolation is a jumping behavior during the deformation of the curve. This phenomenon occurs because the clothoid curve cannot have a cusp, where the curve is kinked or the direction of the curve is abruptly changed. We discuss how to introduce cusps for the log-aesthetic curve including the clothoid curve and propose to use for the representation of a curve the direction angle instead of curvature and define a new curve named τ-curve, which is defined by the direction angle of the curve.
Minimum variation log-aesthetic surfaces and their applications for smoothing free-form shapes
Sho Suzuki,R.U. Gobithaasan,Péter Salvi,Shin Usuki,Kenjiro T. Miura 한국CDE학회 2018 Journal of computational design and engineering Vol.5 No.2
The log-aesthetic curve, which includes the logarithmic (equiangular) spiral, clothoid, and involute of a circle, achieves a control over curvature distribution by defining its shape as an integral form of its curvature and they are expected to be utilized for the field of design. However, it is very difficult to extend it to surfaces and the existing formulations have some problems that they cannot use arbitrary boundary curves. In this paper, we propose ‘‘minimum variation log-aesthetic surface” as a new formulation for the log-aesthetic surface. Based on variational principle our method can generate surfaces by minimizing the objective function newly proposed in this paper for given arbitrary boundary curves.