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

作者：Hu, Gang^*; Bo, Cuicui; Wu, Junli; Wei, Guo; Hou, Fei

来源：Symmetry-Basel, 2018, 10(11): 545.

DOI：10.3390/sym10110545

• SG-Bezier curves
• SG-Bernstein basis function
• continuity condition
• shape parameter
• complex curve design

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 Bezier (or SG-Bezier, 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 G(1 )and G(2) continuity between two adjacent SG-Bezier curves. Furthermore, the detailed steps of smooth continuity for two SG-Bezier curves, and the influence rules of shape parameters on the composite curves, are studied. We also give some important applications of SG-Bezier 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.

• 出版日期2018-11
• 单位西安理工大学