A formulation is introduced that provides a self-consistent, high-frequency description of a wide class of scattering phenomena within a unified framework. This method is based on the appropriate use of locally tangent canonical problems, with a cylindrical uniform configuration and arbitrary cross section. A generalized localization process is applied to define incremental diffracted field contributions, which are adiabatically distributed along the actual edge discontinuities or shadow boundary lines. Then, the total field is represented as the sum of a generalized geometrical optics field plus incremental diffracted field contributions. This representation of the field is uniformly valid at any incidence and observation aspects, including caustics and shadow boundaries of the corresponding ray field description. This method naturally includes the uniform GTD ray field representation of the scattering phenomenon, when it is applicable. For the sake of convenience in the explanation, the formulation for scalar problems is discussed in this paper. The formulation for vector, electromagnetic problems is given in the subsequent paper on electromagnetic formulation. It is suggested that this method may provide a quite general, self-consistent procedure for predicting the field scattered in the near as well as in the extreme far zone of an arbitrarily shaped, opaque object. >