We analyse some recent approaches to the global illumination problem by introducing the corresponding reflection operators, and we demonstrate the advantages of a two-pass method. A generalization of the system introduced by Wallace et al. at Siggraph '87 to integrate diffuse as well as specular effects is presented. It is based on the calculation of extended form-factors, which allows arbitrary geometries to be used in the scene description, as well as refraction effects. We also present a new sampling method for the calculation of form-factors, which is an Mternative to the hemi-cube technique introduced by Cohen and Greenberg for radiosity calculations. This method is particularly well suited to the extended form-factors calculation. The problem of interactive display of the picture being created is also addressed by using hardware-assisted projections and image composition to recreate a complete specular view of the scene.