A frame-based oracle for Hierarchical Radiosity (HR) is proposed which takes into account the Gouraud shading interpolated intensity values mapped from the radiosities. The algorithm is based on a linear approximation of the radiosity function and on the Point Collocation technique. The radiosities are computed at the vertices of the patches which are all triangular. The criterion for the patches subdivision and the interactions refinement is based on the curvature of the intensity distribution along the separating edges between patches of a same surface. The method analyzes the intensity distribution along the edges for each source separately and refines only the interactions with the sources that cause discontinuities. An interaction graph data structure is proposed that allows to isolate the contribution of each source to each vertex. This data structure offers the additional advantage of providing an easy way to isolating the interactions of moving patches in a dynamic environment and only recomputing them at each frame.