The calculation of diffracted fields is considered by means of a geometrical analysis of the incoming wave into semiperiodic zones in the aperture plane, followed by a numerical process for addition of the contributions corresponding to the semiperiodic zones. This general approach constitutes a novel interpretation of diffraction phenomena that permits exact evaluation of the mathematical expressions of diffraction theory and overcomes the limitations of any approximation. The method is illustrated by analysis of two important configuration in optics: the pinhole camera, for which we deduce the optimum radius for imaging, and the diffraction of a spherical converging wave through a circular aperture, from which we determine the limit of the validity of the Fraunhofer approximation (i.e., of the Airy pattern) and the influence of the obliquity factor.