Path tracing preview idea

In reviewing papers from the 1980s I thought again of my first paper submission in 87 or so.  It was a bad idea and rightly got nixed.  But I think it is now a good idea.  Anyone who wants to pursue it please go for it and put me in the acknowledgements: I am working on 2D the next couple of years!

A Monte Carlo ray tracer samples a high dimensional space.  As Cook pointed out in his classic paper, it makes practical sense to divide the space into 1D and 2D subspaces and parametrize them to [0,1] for conceptional simplicity.  For example:

1. camera lens
2. specular reflection direction
3. diffuse reflection direction (could be combined with #3 but in practice don't for glossy layered)
4. light sampling location/direction
5. pixel area
6. time (motion blur)

Each of these can be parametrized not only to [0,1]^2, it can be uniform  by looking at the random number seeds that feed into them.  This yields:

1. (u1, u2)
2. (u3, u4)
3. (u5, u6)
4. (u7, u8)
5. (u9, u10)
6. u11

You can just stratify each of these 2D sets to lower noise and that can help a lot.  For example, generate the first pair so (from Andrew Kensler's paper at Pixar):

All sorts of fun and productive games are played to make the multidimensional properties of the samples for sets across those dimensions, with QMC making a particular approach to that, and Cook suggesting magic squares.  The approach in that bad paper was to pretend there is no correlation at between the pairs of dimensions.   So use:

1. (u1, u2)
2. (u1, u2)
3. (u1, u2)
4. (u1, u2)
5. (u1, u2)
6. u1

 No we have a 2D sampling problem and we can use Warnock style adaptive sampling (wikipedia with figure from the article below)

The samples can be regular or jittered-- just subdivide when the 4-connected or 8-connected neighbors don't match.  Start with 100 or so samples per pixel.

Yes this approach has artifacts, but often now Monte Carlo is used for a noisy preview and the designer hits "go"  for a noisy version when the setup is right.  The approach above will instead give artifacts but the key question for preview (a great area to research now) is how to get the best image for the designer as the image progresses. 

Note this will be best for one bounce of diffuse only but that is often what one wants, and it is another artifact to replace multi-bounce with an ambient.  The question for preview is how best to tradeoff artifacts for time.  Doing it unbiased just makes the artifact noise.

Let me know if anybody tries it.  If you have a Monte Carlo ray tracer it's a pretty quick project.