Abstract: For the pipes modelled by conical surfaces, a method to construct the blending surface consisting of two pieces of toric patches is presented.The parametric domains of toric patches are subdivided into regular decompositions after they are determined by the geometry of pipes.Based on the degeneration of toric patches and the geometric continuity condition between rational Bézier patches, the G¹ continuity condition for control points of the blending surface are derived.The presented method is simple, flexible, and without solving any system of equations.Experimental results are presented that verify the effectiveness of the method.