Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters

In order to solve the problem of geometric design and architectural design of complex engineering surface, we introduce the parametric and geometric continuity constraints of generalized C-Bézier curves and surfaces with shape parameters. Firstly, based on C-Bézier basis with parameters, we study the constraints of the control points of the curves needed to be satisfied when connecting them. Moreover, we study the continuity conditions between two adjacent C-Bézier surfaces with parameters. By the continuity conditions and different shape parameters, the curve and surface can be changed easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve and surface still preserve its characteristics and geometrical configuration. Some graphical examples ensure that the proposed method greatly improves the ability to design complex curves and surfaces and easy to implement.