### A question about BSSRDF generalized to rough surface

Posted:

**Sun May 01, 2016 10:53 am**Hi,

Now I try to implement SSS feature in my renderer using BSSRDF.

I have started with "A Practical Model for Subsurface Light Transport" and Donner's thesis "Towards Realistic Image Synthesis of Scattering Materials".

They say that the diffuse component of BSSRDF for smooth surface ( = ideal specular BTDF?) is

(Screen shot from the former material)

In Donner's thesis they generalize enclosing surface to rough surface, that is

(Screen shot from the latter material)

I'm confused by the symbols used in the latter material.

So, I tried to rewrite what they say by myself.

Here, integration domain H^2- means lower hemisphere (inside material) and I write the diffuse transmittance term by using BSDF(BTDF) instead of BRDF they used.

My understanding for this generalized BSSRDF process is

1. The first integration term represents a total energy entering a material over the interface due to a light coming from wi direction at xi

2. The term R converts the energy to radiant exitance at xo

3. By multiplying 1 /pi to the radiant exitance, we get radiance reaching to xo from any direction in lower hemisphere

4. The second integration term converts the radiance from lower hemisphere to outgoing radiance from xo in direction wo

Is something wrong in my understanding?

Thanks,

Now I try to implement SSS feature in my renderer using BSSRDF.

I have started with "A Practical Model for Subsurface Light Transport" and Donner's thesis "Towards Realistic Image Synthesis of Scattering Materials".

They say that the diffuse component of BSSRDF for smooth surface ( = ideal specular BTDF?) is

(Screen shot from the former material)

In Donner's thesis they generalize enclosing surface to rough surface, that is

(Screen shot from the latter material)

I'm confused by the symbols used in the latter material.

So, I tried to rewrite what they say by myself.

Here, integration domain H^2- means lower hemisphere (inside material) and I write the diffuse transmittance term by using BSDF(BTDF) instead of BRDF they used.

My understanding for this generalized BSSRDF process is

1. The first integration term represents a total energy entering a material over the interface due to a light coming from wi direction at xi

2. The term R converts the energy to radiant exitance at xo

3. By multiplying 1 /pi to the radiant exitance, we get radiance reaching to xo from any direction in lower hemisphere

4. The second integration term converts the radiance from lower hemisphere to outgoing radiance from xo in direction wo

Is something wrong in my understanding?

Thanks,