All of the Sampling Techniques for Paths of Length Two

In bidirectional path tracing, for any path of length k, there are k+2 sampling techniques. Each of these sampling techniques could be used to create exactly the same image, but certain sampling techniques are better at finding certain types of paths. We don't know ahead of time which sampling technique will be the best one for a particular scenario, so instead we use all of the sampling techniques and then combine their results using multiple importance sampling (MIS).

In my bidirectional path tracer I have implemented all of the k+2 sampling techniques for every path length k. Below are renders showing the 4 sampling techniques for paths of length 2. In the captions, s is the number of light subpath vertices in the path and t is the number of eye subpath vertices in the path.

s = 3, t = 0 (direct sensor hits)

s = 2, t = 1 (light tracing with direct sensor sampling)

s = 1, t = 2 (path tracing with direct light sampling)

s = 0, t = 3 (direct light hits)

k = 2, no MIS

k = 2, MIS (correct result but still needs a couple tweaks to be fully tuned)