Radiosity approximates surfaces with polygons and only supports rendering diffuse materials. That's why it supports rendering the image on this slide but not the curvy and glossy surfaces on the next one. At a high level radiosity algorithm does the following: 1. Approximate surfaces using polygons (e.g. triangles or quadrilaterals); 2. For each pair of these polygon patches, compute light reflected from one patch to another based on the relative orientation/position of the two patches (how much of one patch is visible from the other). 3. Repeat step 2 for some number of iterations (until convergence or image looks good enough).