Complete MIS and Optimizations

I finished my multiple importance sampling (MIS) implementation by adding the one missing piece: correct evaluation of the probability density with respect to solid angle of sampling a particular direction from the sensor. I also added a few other important optimizations: Russian roulette for subpath termination, Russian roulette for connecting edge visibility tests, and light emission samples chosen according to the distribution of power over multiple lights. I tested everything very carefully along the way. An important variance reduction technique that I haven't yet implemented is support for special direct illumination strategies.

Below are two images that used the same number of samples and took the same amount of time to render. The difference is that one was rendered with MIS and the other was not (it was rendered by simply weighting the contribution of each path by one over the number of possible sampling techniques for a path of that length). These images illustrate how important MIS is for bidirectional path tracing. The remaining fireflies and severe noise in the MIS image are a result of rare SDS paths that bidirectional path tracing has trouble with. I will soon be implementing MLT in this renderer to help render these types of paths.

Bidirectional path tracing with MIS.

Bidirectional path tracing without MIS.