Global optimization algorithms can be performed to design thinned arrays with various beamshapes. However, they have intensive computational efforts and are therefore limited to small to medium sized array problems. On the other hand, analytical methods do not suffer from this problem, but usually assume an idealized environment, thereby excluding the influence of a complex electromagnetic environment on thinned array designs caused, e.g., by beam-scanning and interference signals. In this paper, a unified framework of the reconfigurable thinned array antenna system is developed and we propose a fast design technique for thinned linear arrays that is capable of dealing with the aforementioned limitations. It is based on the previously published by means of the modified iterative Chirp-Z transform (MICZT) technique, which is herein extended and generalized for linear array thinning with arbitrary grid spacing in the presence of multi-constraint requirements. More specifically, the fast computation of the scannable array factor for a uniformly illuminated thinned linear array is discussed, and beam-scanning thinned arrays with symmetry configuration are also exploited in this paper. In addition, thinned array designs with null placement will be investigated for rejecting multiple sidelobe interference signals. Several representative numerical examples and comparisons with existing methods are presented to validate the effectiveness and efficiency of the proposed technique.