Abstract: In this paper, we discuss GC^k blending problem of two algebraic surfaces of any degree by using the tools of algebraic geometry, obtain some conditions for the existense of blending surfaces of degree p with GC^k continuity. We also deal with some special problems by using the conditions obtained in the paper and derive the corresponding condition and the constructive formulae of blending surfaces. The conditions obtained in this paper are of simple form, easy to be decided and constructive in some interest cases.

Key words: ideal, algebraic surfaces, blending surfaces, ruled sur faces, canonical expansion