A plenoptic camera allows to acquire and separate spatial and directional information of the light coming from a scene. It allows applications such as refocusing at different depths from the one where the image has been acquired. In the literature, different refocusing algorithms are presented for several optical plenoptic configurations. We have previously shown the continuity between these optical designs, and the similarities and differences between the associated algorithms. Here we propose a unique parameterization of the light rays in a plenoptic setup, allowing the development of a unique refocusing algorithm valid for any plenoptic configurations, based on this parameterization. With this method we aim at refocusing images at any distances from the camera, without previous discontinuity due to change of optical configuration. Plenoptic cameras are composed of three optical elements: a main lens, a microlens array and a detector. Two different optical configurations have been presented that differ in the distances between the optical elements. The traditional plenoptic camera has been proposed by Ren Ng in 2005. The focused plenoptic camera was presented by Lumsdaine and Georgiev in 2008. In these articles, both configurations are associated with a dedicated refocusing algorithm with different validity domains corresponding to intervals of distances between the object and the main lens. We have previously presented a comparative study of these two plenoptic systems, considering the optical designs and the refocusing algorithms separately. We have emphasized experimentally the continuity between the optical configurations of the focused and traditional plenoptic cameras, by acquiring raw images of both kinds in our setup. By expressing the refocusing algorithms in the same phase-space diagrams, we have demonstrated that they were based on the same principle, which is the integration of all the directional information for each spatial pixel of the reconstructed image. This analysis justifies the development of a generalized algorithm to unify the processing of plenoptic raw data from both configurations. For this unification, we introduce a mathematical formalism based on the physical properties of the setup and valid for both configurations. It leads to a unique parameterization without discontinuity between the two optical setups, when the distances between the optics or the position of the object change. This formalism points the way towards a unique refocusing algorithm that could be applied to any plenoptic raw data, regardless of the configuration in which they were acquired. In the phase-space, our algorithm corresponds to a generalization of existing algorithms, based on an accurate volume intersection. We aim to obtain reconstructed images visually similar to the results of the other algorithms, but quantitatively more accurate.