关键词: 结式, 代数曲面, 曲面拼接, 同伦变换, Grobner基

Abstract: Three blending methods which are based on resultant theory and homotopy method are presented.Blending equations on algebraic surfaces and their auxillary surface are constructed at first.In fact，computing blending surfaces is the procedure of elimination.Therefore，resultant method is used to blend different algebraic surfaces because of its high efficiency.These three different methods are serial blending method，direct blending method and algebraic surface lifting blending method，for blending three or more surfaces.In these three methods，the first is only suitable for blending two surfaces in turn and there is no intersection between any two different blending surfaces；as to the second method，the blending result is complicated though it is a general algorithm；the last one is a good method，because it is general and the degree of blending surface is much lower than the second method.All of these methods are based on resultant theory.Therefore，the blending surface are obtained after eliminating the new added variables in unit interval and don’t care about the original variables in algebraic equations.Because of these，the complexity of algorithm is low.Moreover，the times of computation can be defined in advance when blending algebraic surfaces.

Key words: resultant, algebraic surface, blending, homotopy transformation, Grobner bases