Bonjour hellfire,
Here I have a theoric explanation. I don't know where I found it, maybe on this forum. And I don't remember who wrote it, I just copy/pasted it into my personal files. Here it is:
Global illumination here refers to computing indirect light, that is,
light that reaches the illuminated point not directly but through an
interaction with another object or medium. (Strictly speaking this
definition would include colored shadows from semi-transparent objects,
but there are easier ways to handle that so we can exclude it here.)
Generally, global illumination normally handles all possible light
interactions: diffuse, glossy, and specular. XSI (mental ray) uses the
photon map algorithm for computing global illumination. It works by
casting photons (light flux packets) from light sources into the scene,
and recording how they bounce and get absorbed.
When computing the brightness of an illuminated point, one can then
look around and check the local recorded photon density. Unfortunately
this method has a problem: unless a lot of photons are used, and the
scene has no hard-to-reach corners, there may not be enough photons in
the vicinity to allow an accurate estimation. This causes noise.
Final gathering is a method to avoid this. It doesn't look for photons
at the illuminated point, but casts a large number of probe rays in a
hemisphere over the illuminated point, and averages the light (including
photons) at the endpoints of these rays. Effectively, this acts as a
one-step "buffer" between the direct and indirect light algorithms.
In practice, there are some limitations. Since final gathering involves
lots of rays, you don't want to do it very often, and certainly not for
every illuminated point. This is where the "safety radius" comes in; it
limits when a neighboring fg point is still usable. There are all kinds
of optimizations that are done here. Also, final gathering is not limited
to one step (this decision is made by shaders in mental ray), which blurs
the line between fg and traditional path tracing a bit.
Sometimes, "first bounce" is enough, and you can just do final gathering
without photon mapping. If a Light L illuminates object A, which sends
some light to B, which illuminates your point in question P, and you are
happy with disregarding the influence of A, you can use final gathering
without photon mapping. It's not accurate but often good enough.
In other words, true global illumination computes LP + LBP + LABP. LP
is direct light to P, LBP is indirect light from B to P (computed by fg
if enabled), and LABP is what you need photon mapping for (or multi-step
fg as I said above, but that can be expensive and can't see zero-area
lights). Of course, there may be more than one A here. fg alone computes
only LP + LBP, but these are usually the most important terms.
Hope this helps
Salutations - Cheers
Bernard Lebel