## “Importance Sampling of Many Lights” - paper: participating media

Practical and theoretical implementation discussion.
b_old
Posts: 12
Joined: Fri Mar 16, 2018 10:30 am

### “Importance Sampling of Many Lights” - paper: participating media

http://aconty.com/pdf/many-lights-hpg2018.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?

graphicsMan
Posts: 167
Joined: Mon Nov 28, 2011 7:28 pm

### 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 Gram-Schmidt 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 $$v_0, v_1$$.

b_old
Posts: 12
Joined: Fri Mar 16, 2018 10:30 am

### 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: