Final Gathering. No, it's not the name of yet another horror movie sequel (although Google isn't much help for figuring out what it in fact is).
It's a technique for effectively smoothing noise in global illumination from Lambertian surfaces. Basically, given a solution to global illumination (like radiosity or a photon map) instead of looking up the diffuse light value in the GI solution, you do one final bounce of light by shooting rays out across the hemisphere above the point you are rendering. These rays sample the secondary light that would be hitting this point much like a distribution raytracer would send out rays to sample the BRDF. In this case, a random sampling of the Lambertian distribution is not the best bet (according to Jensen anways). It is better to use a grid of points placed across the hemisphere according to Lambert's cosine law and then jitter these points slightly to ensure the full hemisphere gets sampled.
When these rays hit a surface a distribution raytracer would send out more rays to sample the light hitting that surface. In FG, you use the precomputed GI solution instead. So, like shadow rays, FG rays do not bounce. However, FG is intentionally used for Lambertian surfaces (perfectly diffuse surfaces). This means that the hemisphere above the point must be FULLY sampled and that takes a lot of rays. Doing this at every point in the scene is very inefficient.
Enter the irradiance cache. Diffuse lighting changes very slowly across a surface; think of a big white wall in an office (the one exception would be a caustic which is actually a diffuse effect but we'll ignore that for now). Slowly changing functions don't need to be sampled as frequently as quickly changing functions so re-computing the FG value at every point across a large surface is wasteful. Instead, we could sample it sparsely and use interpolation of nearby values to fill-in the gaps. This technique is known as irradiance caching and the math behind it is pretty intense.
We still have noise in our simulation and the best way to combat this will be with a final gathering step (something that the previous GSoC project had attempted to include but which I believe was not implemented properly). Unfortunately adding FG is going to severely tank our performance during the lighting calculation phase so (time permitting) we are going to also need an irradiance cache to make it work in a reasonable amount of time. The cache itself is quite simple (very similar in fact to a photon map) but the metrics used to determine where a new sample is needed and where a pre-existing one can be used instead are not so simple. Jensen discusses the irradiance cache in full detail in his book (although he never uses the term 'Final Gathering' that I can see) so implementation should be a matter of translating all the summations and integrals into effective code.
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Info about progress on my Google Summer of Code 2009 project on Advanced Lighting & Shading in CrystalSpace.
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