We present a model-based parallel algorithm for origin and orientation refinement for 3D reconstruction in cryoTEM. The algorithm is based upon the Projection Theorem of the Fourier Transform. Rather than projecting the current 3D model and searching for the best match between an experimental view and the calculated projections, the algorithm computes the Discrete Fourier Transform (DFT) of each projection and searches for the central section ("cut") of the 3D DFT that best matches the DFT of the projection. Factors that affect the efficiency of a parallel program are first reviewed and then the performance and limitations of the proposed algorithm are discussed. The parallel program that implements this algorithm, called PO(2)R, has been used for the refinement of several virus structures, including those of the 500 Angstroms diameter dengue virus (to 9.5 Angstroms resolution), the 850 Angstroms mammalian reovirus (to better than 7A), and the 1800 Angstroms paramecium bursaria chlorella virus (to 15 Angstroms).