We propose to use topological beam tracing to precompute relevant energy exchanges  and visibility in a 3D scene
with general diffuse surfaces.  Shape of the reflected beams is adapted to the reflecting surface reflectance function. 
Light intereflections between a source and surfaces visible from the camera viewpoint are
represented by a sequence of polygons. The visible polygon of the sequence is meshed and illumination is computed 
at vertices using a  Monte-Carlo integration approach.
This combined beam-tracing/Monte-Carlo approach allows for a fast identification of relevant exchanges and
for a variance reduction in the Monte-Carlo estimator. All types of exchanges are simulated.
The global illumination solution can be computed with a coarse mesh and important irradiance discontinuities
can be retreived and inserted in the mesh for high quality display.

Glossy reflections and caustics
 

Soft shadows and diffuse reflection