The generalized H-Bezier model: Geometric continuity conditions and applications to curve and surface modeling

Abstract

The local controlled generalized H-Bezier model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is owed to its good geometric properties, e.g., symmetry and shape adjustable property. In this paper, some geometric continuity conditions for the generalized cubic H-Bezier model are studied for the purpose of constructing shape-controlled complex curves and surfaces in engineering. Firstly, based on the linear independence of generalized H-Bezier basis functions (GHBF), the conditions of first-order and second-order geometric continuity (namely, G1 and G2 continuity) between two adjacent generalized cubic H-Bezier curves are proposed. Furthermore, following analysis of the terminal properties of GHBF, the conditions of G1 geometric continuity between two adjacent generalized H-Bezier surfaces are derived and then simplified by choosing appropriate shape parameters. Finally, two operable procedures of smooth continuity for the generalized H-Bezier model are devised. Modeling examples show that the smooth continuity technology of the generalized H-Bezier model can improve the efficiency of computer design for complex curve and surface models.