Continuity Conditions for Cubic Quasi-Bézier Curves and Surfaces

Focusing on the fact that the engineering complex curves or surfaces can not be described by using a single curve or surface,the continuity conditions of cubic quasi-Bezier(cubic Q-Bezier)curves and surfaces with shape parameters are investigated.Following the analysis of basis functions and terminal properties,the necessary and sufficient conditions of G1,G2 continuity and C1,C2 continuity between two adjacent cubic Q-Bezier curves are proposed.And then,the geometric model of the cubic Q-Bezier surfaces is constructed and the condition of G1 continuity between two adjacent cubic Q-Bezier surfaces in u and v directions is derived and simplified by choosing the control parameters properly.The modeling examples illustrate that the continuity condition of the cubic Q-Bezier curves and surfaces can be widely applied to the complex curves and surfaces modeling system.