Finite Element methods are well suited to the computation of the light distribution in mostly diffuse scenes, but the resulting mesh is often far from optimal to accurately represent illumination. Shadow boundaries are hard to capture in the mesh, and the illumination may contain artifacts due to light transports at different mesh hierarchy levels. To render a high quality image a costly final gather reconstruction step is usually done, which re-evaluates the illumination integral for each pixel. In this paper an algorithm is presented which significantly speeds up the final gather by exploiting spatial and directional coherence information taken from the radiosity solution. Senders are classified, so that their contribution to a pixel is either interpolated from the radiosity solution or recomputed with an appropriate number of new samples. By interpolating this sampling pattern over the radiosity mesh, continuous solutions are obtained.