Radiation integral areas are localized and reduced based upon the locality of scattering phenomena. In the high frequency, the scattering field is given by the currents, not the entire region, but on the local areas near the scattering centers, such as the stationary phase points and edge diffraction points, due to the cancelling effect of integrand in the radiation integral. The numerical calculation which this locality is implemented into has been proposed for 2-dimensional problems. The scattering field can be approximated by integrating the currents weighted by the adequate function in the local areas whose size and position are determined appropriately. Fresnel zone was previously introduced as the good criterion to determine the local areas, but the determination method was slightly different, depending on the type of scattering centers. The objective of this paper is to advance the Fresnel zone criteria in a 2-dimensional case to the next stage with enhanced generality and applicability. The Fresnel zone number is applied not directly to the actual surface but to the virtual one associated with the modified surface-normal vector satisfying the reflection law. At the same time, the argument in the weighting function is newly defined by the Fresnel zone number instead of the actual distance from the scattering centers. These two revisions bring about the following three advantages; the uniform treatment of various types scattering centers, the smallest area in the localization and applicability to 3-dimensional problems.