G¹ Continuity of C-Bezier Rectangular Surfaces

This paper probes G¹ continuity between two adjacent c-Bezier rectangular patches. The necessary and sufficient conditions are derived. It shows that the coplanar condition for G¹ continuity of two adjacent Bezier patches is not necessary for c-Bezier patches. Such a relaxation of constraints on control points is beneficial from vector weights of c-Bezier surfaces, which leads to two extra free design parameters for each control point. C-Bezier surfaces offer the possibility of obtaining G¹ continuity by just adjusting the weights, which greatly simplifies the design to construct composite surfaces.