A personal annotations of Veach's thesis (20) pp.310-321

p.310 Special cases for short subpaths

There are zero subpaths vertices and one path vertices to generate subpaths. If I draw a picture, there is one line from the lens to the light source. So, I could not distinguish the difference. Again, I asked my friend/specialist. It is quite convenient to have such friends, but, I should study more, otherwise, these friends will be bothered by me. The correct picture is shown in Figure 1.

     Figure 1. Short subpath

The differences are:

  • Zero subpath vertices: The sample is done from the lens only, the probability is only related with lens, and it coincidentally hit to a light source.
  • One subpath vertices: The sample is done on the light source with sample density probability only. Then this vertex is connected to the lens.

The path's generation probability is not the same, therefore, the contribution is also not the same.

Thanks to Leo and Carsten.

p.321 Implementation

It's a bit details, but I have a question in the following equation.

I computed this as follows.

I may have a mistake. Actually, today I write 3 - 4 = 1 and my matrix becomes unsolvable when I try to get a row reduced echelon form. I was astonished when I compare my calculation and the output of the octave. But, still where is N_0?

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