The crystallographic fast Fourier transform. III. Centred lattices

Algorithms for evaluation of the crystallographic FFT for centred lattices are presented. These algorithms can be applied to 80 space groups containing centring operators. For 44 of them, combining these algorithms with those described by Rowicka, Kudlicki & Otwinowski [Acta Cryst A59, 172-182] yields the maximal symmetry reduction. For other groups, new algorithms, to be presented in our forthcoming paper [Rowicka, Kudlicki & Otwinowski (2003), in preparation], are needed. The requirements on the grid size and how they interact with the choice of algorithms are also discussed in detail.