In order to overcome the difficulty in applying the Catmull-Clark subdivision surfaces in engineering

a new algorithm about Catmull-Clark subdivision surfaces based on C-B splines is presented. C-B splines curves are extension of B splines

they depend on a parameterα. By use of characteristics of C-B splines

for example

they can provide exact reproduction of circles and cylinders and they can be generated by subdivision scheme while keepingC2

a new surface scheme is generated. The limit surfaces generated by this surface scheme areC2except at extraordinary points. In conclusion

this method not only solves the problem of the precise representation of standard analytic shapes such as circle encountered by Catmull-Clark subdivision surfaces

but also overcomes the difficulty of generating surfaces on arbitrary topological meshes faced by NURBS. Meanwhile

the shaapes of the subdivision surfaces can be adjusted using controlling parameterαand the particular case (α→0) of this scheme is Catmull-Clark subdivision scheme. An application in engineering garphics demonstrates freedom and efficiency of this algorithm.