This paper proposes a deterministic method for the 3D synthesis of antenna arrays that jointly accounts for far-field pattern reconfigurability, polarization setting, dynamic range ratio reduction, and near-field control. The conceived algorithm, which generalizes some existing solutions, relies on a weighted cost function, whose iterative minimization is accomplished by properly derived closed-form expressions. This feature, combined with the possibility of selecting the weighting parameters, provides a fast and versatile approach, whose capabilities are numerically checked by considering different synthesis problems and array structures in the presence of mutual coupling.