In this paper we present a new framework for subdivision surface fitting of arbitrary surfaces (not closed objects) represented by polygonal meshes. Our approach is particularly suited for output surfaces from a mechanical or CAD object segmentation for a piecewise subdivision surface approximation. Our algorithm produces a mixed quadrangle-triangle control mesh, near optimal in terms of face and vertex numbers while remaining independent of the connectivity of the input mesh. The first step approximates the boundaries with subdivision curves and creates an initial subdivision surface by optimally linking the boundary control points with respect to the lines of curvature of the target surface. Then, a second step optimizes the initial control polyhedron by iteratively moving control points and enriching regions according to the error distribution. Experiments conducted on several surfaces and on a whole segmented mechanical object, have proven the coherency and the efficiency of our algorithm, compared with existing methods.