A Note on Superspirals of Confluent Type

Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function. They are generalizations of log-aesthetic curves, and other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. In this work, we study superspirals of confluent type via similarity geometry. Through a detailed investigation of the similarity curvatures of superspirals of confluent type, we find a new class of planar curves with monotone curvature in terms of Tricomi confluent hypergeometric function. Moreover, the proposed ideas will be our guide to expanding superspirals.

Style Design System Based on Class A Bézier Curves for High-Quality Aesthetic Shapes

In this paper, a style design system in which the conditions for Class A Bézier curves are applied is presented to embody designer’s intention by aesthetically high-quality shapes. Here, the term “Class A” means a high-quality shape that has monotone curvature and torsion, and the recent industrial design requires not only aesthetically pleasing aspect but also such high-quality shapes. Conventional design tools such as normal Bézier curves can represent any shapes in a modeling system; however, the system only provides a modeling framework, it does not necessarily guarantee high-quality shapes. Actually, designers do a cumbersome manipulation of many control points during the styling process to represent outline curves and feature curves; this hardship prevents designers from doing efficient and creative styling activities. Therefore, we developed a style design system to support a designer’s task by utilizing the Class A conditions of Bézier curves with monotone curvature and torsion.