Aesthetic shapes are usually actualized as 3D objects represented by free-form surfaces. The main components used to achieve aesthetic surfaces are 2D and 3D curves, which are the elements most basic for determining the shapes and silhouettes of industrial products. Bézier, B-Spline and NURBS are types of flexible curves developed for various design intents. These curves, however produce complex curvature functions that may undermine the formulation of shape aesthetics. A viable solution to this problem is to formulate aesthetic curves and surfaces from well-defined curvatures to improve aesthetic design quality. This paper advocates formalizing aesthetic curve and surface theories to fill the gapmentioned above, which has existed since the 1970s. This paper begins by reviewing on fair curves and surfaces. It then extensively discusses on the technicalities of Log-Aesthetic (LA) curves and surfaces and touches on industrial design applications. These emerging LA curves have a high potential for being used as standards to generate, evaluate and reshape aesthetic curves and surfaces, thus revolutionizing efficiency in developing curve and shape aesthetics.

This paper elucidates the possibilities to interactively generate and deform Logaesthetic (LA) curves regardless of their integral form. The methods proposed are twofold; in the first section, we propose new method to generate an S-shaped LA spline. In the next section, we propose a novel method to solve the G 2 Hermite interpolation problem with LA curves which is in the form of LA triplets. These methods have been implemented as a plug-in module for a commercial CAD system and are successfully used for practical design. This paper proofs that LA curve has matured and ready for industrial design.

The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. The discrete log-aesthetic filter based on the formulation of the log-aesthetic curve has successfully been introduced not to impose strong constraints on the designer's activity, to let him/her design freely and to embed the properties of the log-aesthetic curves for complicated ones with both increasing and decreasing curvature. In this paper, in order to define the log-aesthetic surface and develop surface filters based on its formulation, at first we reformulate the log-aesthetic curve with variational principle. Then we propose several new functionals to be minimized for free-form surfaces and define the log-aesthetic surface. Furthermore we propose new discrete surface filters based on the log-aesthetic surface formulation.

No abstract

The main characteristic of visually pleasing curves used for product design is a monotonic curvature profile. Recently, a planar curve called Generalized Log Aesthetic Curve (GLAC) has been extended from the Log Aesthetic Curve (LAC), and it has an additional shape parameter,ν. This curve preserves the monotonicity of curvature and is said to produce visually pleasing curves. This paper delves on the drawable region of the GLAC segment which indicates the probable solutions of shape parameters from given interpolating points and the direction of travel at those points. The first section reviews the formulation of GLAC and its related bounds. The section describes the algorithm for identifying the drawable region. It is followed by the section describing how small changes ofνwiden the drawable boundaries. The final section discusses the superiority of GLAC compared to LAC for use in industrial product design.