Question about 'Hemispherical Guiding with Spherical Distributions' about robust-vmm-guiding HOT 5 CLOSED

The m_distributions[0] is actually an entire mixture of up to 32 components.
For the BSDF product, I may have to compute the product with 2 components
which then results in two mixutres m_distributions[0] and m_distributions[1] which essentially combine into a mixture of up to 64 components.

The product function I've linked above is the wrong one.
This one will be called:

from robust-vmm-guiding.

Hi,
of course, all vMF distributions span the entire sphere - so when sampling them without bias, there are necessarily always a few samples below the hemisphere.
However, when we sample a vMF mixture, we already know our intersection point and its surface normal.
So, instead of sampling the mixture as is, we compute the product of each component with a vMF approximation of the cosine lobe centered around that surface normal.
(Each component will also be weighted by the integral of that product.)
The resulting mixture will be focused much more towards directions on the upper hemisphere and far less towards the lower hemisphere.
Essentially, its the cheapest way of product sampling you can do:
In this case, we only consider the cosine term in the rendering equation.

The relevant code is here:

I hope that is clear enough, I feel like this needs some drawing to come across :)

Best regards,
Lukas

from robust-vmm-guiding.

OMG, "a vMF approximation of the cosine!" -> That makes sense because the product of two vMF-lobes is as straightforward as your paper described in Appendix A.1, isn't it?
When I first read the paper, I was confused about multiplying the vMF with the cosine. But now I understand that you're multiplying it after approximating the cosine as another vMF. Thank you for explaining it so quickly and clearly.

from robust-vmm-guiding.

Additionally, I'm wondering why only the first lobe (gBSDF.m_guidingData.m_distributions[0]) is used when sampling the cosine product in GuidingDistributionFactoryVMM.h.

from robust-vmm-guiding.

Thank you very much!!

from robust-vmm-guiding.