Abstract: We analyze some recent approaches to the global illumination problem by introducing the corresponding $<$i$>$reflection operators$<$/i$>$, and we demonstrate the advantages of a two-pass method. A generalization of this system introduced by Wallace $<$i$>$et al.$<$/i$>$ at SIGGRAPH 87 to integrate diffuse as well as specular reflection is presented. It is based on the calculation of $<$i$>$extended form-factors$<$/i$>$, 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 alternative to the $<$i$>$hemi-cube$<$/i$>$ 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.