Aesthetic Curves and Surfaces in Computer Aided Geometric Design

Abstract

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.