This paper focuses on a new radiosity approach. Using a new geometrical model that describes any surface with an atlas of ``disk-like patches'', i.e. a set of pieces covering the surface that can overlap each other, we express the radiosity function in a new function base. This leads to a new radiosity system where overlapping areas are taken into account. The classical radiosity approach appears now as a particular limit case of this new ``overlapping radiosity''.