Since radiance in a vacuum remains constant along rays, the radiance in a scene's free space can be represented as a real function over the space of maximal segments. This space is four dimensional and organized by the visibility complex. To date only the 0-D and 1-D cells of the visibility complex have been constructed and implemented. In order to use this topological space to support radiance samples for image-based rendering, form-factor computations, global illumination and shadowing, we also need to construct its 2-D cells. This paper expands the frontier of our understanding of the visibility complex by constructing and implementing its 2-D cells. We demonstrate the capabilities of these 2-cells by using them to organize sparse illumination samples in a scene. These samples interpolate only within the boundaries of the 2-cells, thus avoiding aliasing while respecting sharp changes in illumination.