*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.
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