Ball Said-Ball curve: Construction and its geometric algorithms. (December 2022) - Hu, Gang; Du, Bo
Highlights: A method of design for ball Said-Ball (BSB) curve is proposed. The geometrical properties and algorithms of BSB curve are investigated. The conditions for G 1 and G 2 continuity of BSB curves are obtained. An extension method of BSB curve with minimum energy is presented. A novel BSB rotation surface with thickness is constructed. Abstract: The representation method of curves and surfaces is an essential tool in industrial design, while a ball curve with adjustable thickness has its advantages in representing freedom tubular objects. By combing the Said-Ball basic functions and the control balls, this paper constructs the ball Said-Ball (BSB, for short) curve and discusses the related geometrical properties and algorithms. Then, the G 1 and G 2 continuity conditions between two adjacent BSB curves are discussed. Furthermore, on the premise of G 2 continuity, an extension method of the BSB curve with minimum energy is studied. For this method, the GaussNewton-NL2SOL algorithm is used to obtain the best scale parameters of the center curve. Meanwhile, the optimal parameters of the radius function are also determined by solving the extreme. Finally, the construction of the BSB rotation surface with different continuity is given. The provided modeling examples show that the BSB curve with thickness is more suitable and valuable in the design for the modeling of objects, on the premise of maintaining excellent geometric properties.