G1 Smoothing Solid Objects by Bicubic Bezier Patches

A general and unified method is presented for generating a wide range of 3-D objects by smoothing the vertices and edges of a given polyhedron with arbitrary topology using bicubic Bezier patches. The common solution to the compatibility equations of $G^1$ geometric continuity between two Bezier patches is obtained and employed as the foundation of this new method such that this new solid and surface model is reliable and compatible with the solid modeling and surface modeling systems in the most common use. The new method has been embedded in an algorithm supported by our newly developed solid modeling system MESSAGE. The performance and implementation of this new algorithm show that it is efficient, flexible and easy to manipulate.