I'm reading and implementing a paper about Importance Sampling of Many Lights with Adaptive Tree Splitting.
http://aconty.com/pdf/manylightshpg2018.pdf
In section 5.2 on cluster importance for participating media, there is a part that I don't understand: How do they compute the vectors o1, o2? I don't understand the paragraph explaining how to obtain this basis from v1, v2. Can anyone explain it?
“Importance Sampling of Many Lights”  paper: participating media

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Re: “Importance Sampling of Many Lights”  paper: participating media
Okay, I haven't read through the paper, but my understanding from the surrounding context is that you are already given \(v_0\) and \(v_1\). You use those to compute an orthonormal basis. \(o_0\) and \(o_1\) will be orthogonal unit vectors in the same plane as \(v_0\) and \(v_1\). \(o_0 = v_0/v_0\) and \(o_1\) will be an orthogonal unit vector. Essentially, you can use the normalized cross product of \(v_0\) and \(v_1\) to have an ortho vector to both of \(v_0, v_1\), call it \(v_2\). Finally you could take another cross product of \(o_0\) and \(v_2\) to get \(o_1\).
You could also use GramSchmidt orthonormalization.
Again, didn't read the paper, so I may be off somewhere, but judging based on that section, I think \(o_0, o_1\) is just a pair of basis vectors in the same plane as \(v_0, v_1\).
You could also use GramSchmidt orthonormalization.
Again, didn't read the paper, so I may be off somewhere, but judging based on that section, I think \(o_0, o_1\) is just a pair of basis vectors in the same plane as \(v_0, v_1\).
Re: “Importance Sampling of Many Lights”  paper: participating media
Thanks for your explanation, I think I understand the section better now!
I had also started a conversation on [computer graphics stack exchange, which might be helpful:
https://computergraphics.stackexchange.com/questions/10269/importancesamplingofmanylightswithadaptivetreesplittingpaperparti/10276?noredirect=1#comment16095_10276
I had also started a conversation on [computer graphics stack exchange, which might be helpful:
https://computergraphics.stackexchange.com/questions/10269/importancesamplingofmanylightswithadaptivetreesplittingpaperparti/10276?noredirect=1#comment16095_10276