Zone plates and photon sieves can be used to focus soft X-rays and hard X-rays. Relative to the parallel plane wave incidence and focusing on the optical axis, we here present two different models to describe the other kinds of focusing properties. The former, the scaled zone plates or photon sieves are appropriate for the titled plane wave to image, which can alter the propagation direction. The latter, the eccentric elliptical zone plates or photon sieves are appropriate for the point-to-point off-axis focusing. Based on the above-mentioned models, the different algorithms are discussed in detail under the condition of different numerical apertures. Furthermore, the correctness of our model has been verified through the commercial software VirtualLAB. The obtained results can be used for the analysis, design, and simulation of different zone plates and photon sieves, meanwhile the non-coaxial characteristics can increase the flexibility of the optical system.