Two main goals were tried to realize. One was to make the shape of the cubic uniform B-spline curve and surface can be adjusted freely under the condition of without changing the control points. The other was to make the curve and surface can easily achieve interpolation in the case of did not need to reverse compute control points. To achieve these aims, a kind of blending function, which contains two groups of parameters, was constructed in the polynomial function space. Based on the blending function, the polynomial curves were defined, which on four-point piecewise scheme and the corresponding tensor product surfaces. The blending function contained the cubic uniform B-spline basis function as a special case. One set of parameters of the blending function determine the endpoint position of the curve and the corner point position of the surface. While another set of parameters control the tangent vector of the curves at the endpoints and of the surfaces at the corner points. By choosing appropriate parameters, the curves and surfaces were located within the convex hull of the control points, or interpolate the inner control points. As a result, with only one model, the uniform representation is achieved, which of the curves and surfaces for approximating and interpolating the control polygon and control net. The numerical experimental results show the correctness and effectiveness of the method.