Abstract: In this paper, a set of rational polynomial functions with five parameters are proposed to achieve the following two goals:1) make curve and surface achieve higher order smoothness by joining under relatively simple conditions, and 2) adjust their shape freely without changing the positions of control points.Based on the proposed polynomial functions, we define a new curve determined by four control points and a new surface determined by sixteen control points.The smooth join conditions of the new curve and surface are discussed.According to the continuity conditions, we define a piecewise combination curve and surface consisting of the new curve and surface.Our method automatically ensures the continuity of the resulting curve and surface.Experimental results show the effectiveness of the method.