Gröbner Basis Methods for Algebraic Blending Surfaces in CAGD

The research on constructing algebraic blending surfaces between given surfaces is one of the most important problems in geometric modeling and computer graphics. To solve the problem better, this paper gives novel methods using theories of Gröbner bases to construct the required blending surfaces. According to the main theorems, we obtain the algorithms for constructing the blending surface, which meets the given surfaces with G, G, or G continuity along given algebraic curves and has lower degree. Finally, some examples are given to illustrate the correctness and efficiency of our methods.