The manipulation of the near field (NF) is a challenging topic of electromagnetics, carrying essential importance for several applications. In this work, we develop an algorithm capable of shaping the near field in 3D domains according to given specifications. The algorithm is based on a set theoretic approach and a front-and-back iterative propagation scheme. The latter is realized using Fast Fourier Transforms (FFT), reducing the required computational time. The algorithm is applied on a focal shaping scenario. In this case, a full control of the depth of focus, spot diameter and sidelobe level of the generated radiation is achieved. In particular, the proposed procedure is successfully adopted to control the normal component of a radiating aperture over a range of 12 at 30 GHz. The derived aperture field distribution is then synthesized by a Radial Line Slot Antenna (RLSA) by means of an in-house Method of Moments (MoM) code. Near-field measurements have validated the proposed approach and prototype.