3D Class A Bézier curves with monotone curvature. (June 2023)

• Record Type: Journal Article
• Authors: Wang, Aizeng; He, Chuan; Zheng, Jianmin; Zhao, Gang
• Is Part Of: Computer aided design. Volume 159(2023)
• Publication Date: 2023-06
• Subjects: Class A curves -- Bézier curves -- Monotonic curvature -- Aesthetic shape design; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2023.103501
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: This paper introduces a special class of 3D Bézier curves that are defined by their degree, a starting point, the first leg of their control polygons, and a 3D affine transformation composing of a uniform scaling and a rotation. We present new formulas for the curvature of such Bézier curves and based on the new formulas we derive sufficient conditions for the curves to have monotonic curvature. The conditions are expressed by a simple constraint on the rotation angle and the scaling factor. This facilitates constructing 3D Class A Bézier curves that are a generalization of planar typical curves proposed by Mineur et al. (1998), which are often used in automotive and other design applications. Some examples are provided to demonstrate the effectiveness of our construction. Highlights: This paper presents a class of 3D Bézier curves of arbitrary degree with monotone curvature. It is a generalization of planar typical curves proposed by Mineur et al. (1998). We derive a sufficient condition for a 3D Bézier curve to belong to this class .