Image-based rendering (IBR) has become a very active research area in recent years. The optimal sampling problem for IBR has not been completely solved. In this paper, we show that theoretically, the optimal sampling efficiency can be achieved by employing the generalized periodic sampling theory with arbitrary geometry. When there is no occlusion in the scene and the scene is Lambertian, we show that the sampling density can be twice of that when we use rectangular sampling. We then propose a general framework for IBR sampling. Begin with an over-sampled dataset, we down-sample the data first in the discrete domain. To render an image from the down-sampled data, two approaches are proposed, i.e., to reconstruct the oversampled dataset first through up-sampling and then rendering, or to use a continuous interpolation filter to calculate the desired light rays directly. Eigenfilter method is employed to design filters during downsampling and up-sampling. We show that if the proposed approach adopts the same down-sampling density as the previous work, the reconstruction filter of the proposed approach is easier to design, and the reconstructed scene could have a higher quality. However, in practice rectangular sampling has several advantages over generalized sampling. We analyze the pros and cons for each sampling approach, and explain why in practice rectangular sampling is still more preferable.