This study investigated how the choice of fixed planes for the representation of the projection data of a cylindrical positron emission tomography (PET) scanner simplifies the frequency interpolation required by the 3D Fourier slice theorem (3D-FST). A new gridding algorithm based on a two-plane geometry and requiring only 1D interpolations in the Fourier domain was compared with the direct implementation of the 3D-FST. We show that the use of two orthogonal planes leads to signal to noise ratios similar to those achieved with the 3D-FST algorithm from projection data acquired with up to two times more count rates, while the resolution remains similar.