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Lecture 13: Global Illumination and Path Tracing (21)
jeromylui

So for the importance sample BDRF, we are told that BRDF is 4 dimension function, but if we fix omega r, BRDF will only vary over incoming directions, so it’ll be a 2 dimensional function on the hemisphere. Then we draw samples from that distribution function. I just wanted to clarify, does that mean that we sample from 2 random variables? And in this case, what are the random variables?

moridin22

You're right that there are two dimensions left after we fix $\omega_r$, but the only other variable we have to sample is $\omega_j$, which is also two-dimensional.

jsc723

Why do we want to sample proportional to BRDF? Is there any intuition behind that?

yzyz

For non-diffuse materials, light rays won't be reflected equally in all directions, so it's worth doing importance sampling on the BRDF in order to sample the directions light likely came from. So by sampling proportional to the BRDF, our estimator will converge faster since it doesn't have to waste as much computation time on unlikely directions.

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