The unique concept of the modified edge representation (MER) was proposed for the surface to the line integral reduction of the physical optic (PO). The equivalence between the MER line and the PO surface integration was analytically derived by using the Stokes theorem relations as well as asymptotic treatments, for the smooth scattering surfaces without inner stationary phase points (SPP). Later on, for the planar surface, the MER line integration around the inner SPP was investigated, and it was identified as the scattering geometrical optics (SGO). In this paper, findings related with the MER line integration around the inner SPP are extended to curved surfaces. The accuracy and the applicability of the SGO extraction in terms of the MER line integration are numerically investigated for different radii of curvatures of the scattering surfaces. Authors introduce a geometrical criterion for the applicability of the method. The MER line integration provides an alternative way to the stationary phase method or the classical geometrical optics for calculating SGO. In addition, this numerical result indirectly identifies the entity of the MER line integration along the periphery of the scattering illuminated region, irrespective of the position of observer, as not other than diffraction.