Modeling of Free-Form Complex Curves Using SG-Bézier Curves with Constraints of Geometric Continuities

Symmetry

Fei Hou¹  Gang Hu²  Junli Wu²  Cuicui Bo²  Guo Wei³ 

[1] Computer Science, University of North Carolina at Pembroke, Pembroke, NC 28372, USA;Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China;;Department of Mathematics &

关键词: SG-Bézier curves;    SG-Bernstein basis function;    continuity condition;    shape parameter;    complex curve design;   

DOI  :  10.3390/sym10110545

来源: DOAJ

【 摘 要 】

The modeling of free-form engineering complex curves is an important subject in product modeling, graphics, and computer aided design/computer aided manufacturing (CAD/CAM). In this paper, we propose a novel method to construct free-form complex curves using shape-adjustable generalized Bézier (or SG-Bézier, for short) curves with constraints of geometric continuities. In order to overcome the difficulty that most of the composite curves in engineering cannot often be constructed by using only a single curve, we propose the necessary and sufficient conditions for G¹ and G² continuity between two adjacent SG-Bézier curves. Furthermore, the detailed steps of smooth continuity for two SG-Bézier curves, and the influence rules of shape parameters on the composite curves, are studied. We also give some important applications of SG-Bézier curves. The modeling examples show that our methods in this paper are very effective, can easily be performed, and can provide an alternative powerful strategy for the design of complex curves.

【 授权许可】

Unknown