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Proceedings of CAD'17, 2017, 367-373
A New Formulation of the Minimum Variation Log-aesthetic Surface for Scale-invariance and Parameterization-independence

Sho Suzuki, Shin Usuki, Kenjiro T. Miura, Shizuoka University
R.U. Gobithaasan, Universiti Malaysia Terengganu

Abstract. Recently, aesthetic design which takes account of designability has become popular. In the aesthetic design, the creation of High quality curve and surface models is demanded. However, on current CAD systems, the operator must move control points by trial and error to obtain high-quality curves and surfaces. This incurs high costs and requires a great deal of expertise. Therefore, an efficient method to generate fair curves and surfaces is desirable to achieve high quality that will satisfy customers’ aesthetic requirements. The log-aesthetic curve was proposed as a curve which satisfy these quality requirements. Harada et al. defined “Aesthetic curves” as curves whose logarithmic distribution diagram of curvature (LDDC) can be approximated by a straight line. In response to this research, Miura et al. derived analytical solutions of the curves whose logarithmic curvature graph (LCG) as an analytical version of the LDDC is strictly given by a straight line and defined the curve as the log-aesthetic curve. For a given curve, the arc length of the curve and the radius of curvature are denoted by s and rho, respectively.

Keywords. Log-aesthetic Surface, Minimum Variation Log-aesthetic Surface, Variational Principle, Scale Invariant, Principal Curvatures

DOI: 10.14733/cadconfP.2017.367-373