Given a polygonal mesh with a set of tagged control polygons, a subdivision surface that interpolates the B-spline curves of these control polygons can be obtained by constructing a set of polygonal complexes, each of which converges to one of the given curves.The construction process will geometrically and topologically disturb the initial and/or the subdivided polygonal meshes in the vicinity of the polygonal complexes. This may result in a poorly shaped surfaces across the interpolated curves. Based on signal fairing, this paper describes a method to fair such a surface and paves the way to achieve further constraints such as interpolating curves with predefined tangent plane or cross curvature.