Implementing SpongeCake BSDF: Sampling half-vectors correctly.

[Vrroom]

Hello Everyone,

I'm implementing the SpongeCake BSDF. This is a BSDF that has a symmetric reflecting and transmitting Normal Distribution Function (NDF). I want to ensure that I'm sampling the half vector correctly.

This is what I have so far:

        alpha = dr.maximum(0.0001, self.alpha)
        S = dr.diag(mi.Vector3f(alpha * alpha, alpha * alpha, 1)) # surface type matrix. Later we'll rotate it and all that.
        sh_frame = mi.Frame3f(si.wi)
        # https://mitsuba.readthedocs.io/en/latest/src/api_reference.html#sggx_sample, it seems that
        # the sh_frame is constructed as mi.Frame3f(si.wi). I checked via PDB that this is different from si.sh_frame
        # even if this is correct, the question remains whether the h is in the correct space
        h = sggx_sample(sh_frame, sample2, S)
        wo = mi.reflect(si.wi, h) 

My questions are whether I'm using:

• The correct sh_frame to sample h. Should it be mi.Frame3f(si.wi) or si.sh_frame. I checked via PDB and the two are different.
• What coordinate frame is the sampled h in. The docs referenced say that this is in the world space but based on my understanding of this stuff, I need an h in the local shading frame.

Happy to provide more information. Hope my question is clear. Thanks everyone.

Sumit.

[ziyi-zhang]

Hi,
For surface interactions si, the shading frame is usually mi.Frame3f(shading_normal). But for medium interactions mei, the shading frame is typically mi.Frame3f(mei.wi).
The spongecake BSDF is a special case that entails both concepts: it assumes microflake volume under a surface. You need to be careful not to misuse the frame and the coordinate system. Also note that si.wi is the incident direction in surface normal's local frame, not in world space.
Best

[Vrroom]

Thanks Ziyi. I found the answer to my question but forgot to post it. This is slightly different from your comment. Let me write it here for anyone stumbling into this in the future.

In the case of the SpongeCake BSDF, the phase function f(wi, wo) to be sampled is the specular phase function from the SGGX microflake (See Eq 24 in the linked in the paper). The algorithm sampling from this phase function requires constructing an orthonormal basis around wi (See Algorithm 1 in the SGGX paper). This is why, the correct frame to pass to sggx_sample is sh_frame = mi.Frame3f(si.wi) as in my code above.

In this case, I have erroneously named the orthonormal basis as sh_frame. It is not a shading frame at all. Rather it helps us compute and sample from the Visible (from the direction wi) NDF of the SGGX microflake.

[Vrroom]

Ok. Actually you did kind of say that when you mentioned mei.wi. My bad.