Final Gathering using Ray Differentials

We have developped a method for attaining better quality from the calculations of indirect illumination in photon mapping, used for global illumination. During the photon mapping calculations, the final gathering step has previously sampled the world over areas that have largely been dependant on the distribution of photons. This strategy gives a series of problems that are usually solved by increasing the sampling rate. To reduce these problems, we suggest sampling over the real area, given by the area the ray ought to cover. We calculate the footprint by using ray differentials, and then look up in a precalculated mipmap of estimated irradiance values. By doing this we get a better estimate of the incoming diffuse lighting, which means a more correct image with the same amount of samples. By using a mipmap of irradiance estimates, this enhancement is reached faster than by using regular final gathering