In the present contribution, the strategy of atomic force microscope mapping of periodical rough surfaces is combined with an extension of the polyhedral model. Atomic force microscope images are numerically interpolated, applying non-uniform rational B-splines, which also have the advantage that simultaneously to the interpolation, they provide the normals at any point on the rough surfaces. Compared with the polyhedral model, in the present scheme, any rough surface is accurately well approximated by a finite set of almost infinitesimal planes, which are all oriented in accordance with the normals obtained, while non-uniform rational B-splines interpolate the surface. In this view, the Beer-Lambert law is straightforwardly applied to compute all local (almost pointwise resolved) contributions to the photoelectron intensity on the analyser site. The proposed numerical scheme is validated in case of Si samples possessing either arbitrary rough, one-or two-dimensional periodic structures on the analysed surfaces. In this manner, it is shown that the computed angle-resolved XPS well agree with the experimental ones.