Abstract: Focusing on the problem that the engineering complex surfaces can not be
described by using a single cubic extension Bézier (CE-Bézier) surfaces with multiple shape
parameters, the continuity conditions of CE-Bézier surfaces are proposed. Following the analysis
of basis functions and terminal properties, the unique property of CE-Bézier curves is investigated
and the corresponding conclusion that a CE-Bézier curve can be defined by many different groups
of control points and shape parameters is also obtained. And then, the geometric model of
CE-Bézier surfaces is constructed and the condition of G1 continuity between two adjacent
CE-Bézier 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 CE-Bézier
surfaces can be widely applied to the complex surfaces modeling system.

Key words: CE-Bézier curve, CE-Bézier surface, shape parameter, continuity condition;
analysis of unique property