A new formulation of the minimum variation log-aesthetic surface for scale-invariance and parameterization-independence

ABSTRACT

The log-aesthetic curve, which includes the logarithmic (equiangular) spiral, clothoid, and circular involute, achieves control over the curvature distribution by defining its shape as an integral of its curvature, and is expected to be utilized for the field of aesthetic design.

Some formulations of the log-aesthetic surface as extensions of the log-aesthetic curve have been proposed. The minimum variation surface is one of them, and has a feature that it can be used for arbitrary four boundary curves. The minimum variation log-aesthetic surface is defined as a surface which minimizes an objective function. However, it is not scale-invariant and parameterization-independent.

In this study, we propose a new formulation of the minimum variation log-aesthetic surface for scale-invariance and parameterization-independence.

GRAPHICAL ABSTRACT

KEYWORDS:

• Log-aesthetic surface
• minimum variation log-aesthetic surface
• variational principle
• scale invariance
• parameterization independence

ORCID

Sho Suzuki http://orcid.org/0000-0002-2607-7204

R.U. Gobithaasan http://orcid.org/0000-0003-3077-8772

Shin Usuki http://orcid.org/0000-0003-1165-5507

Kenjiro T. Miura http://orcid.org/0000-0001-9326-3130