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### #ActualHodgman

Posted 25 February 2013 - 07:36 PM

I might be getting a bit off topic now... forgive me

I went to bed last night with Helmholtz reciprocity on my mind -- apparently our physically based BRDF's should all obey this law, that if you swap a light source and a camera, you'll measure the same ray of light in either configuration, or in the case of our BRDF's, swapping L and V has no effect.

The thought experiment that caused me lost sleep was an optically-flat Lambertian diffuse plane (i.e. all microfacets are aligned with the normal, all refracted light is uniformly dispersed over the upper hemisphere), with the two observation/lighting angles being directly overhead (0º from the normal) and very nearly perpendicular (~90º).

When lit from above and viewed from the side, the majority of the light will be refracted into the surface and then diffused -- no matter where the camera is in the hemisphere, the surface will appear the same. The camera will receive a small percentage of the diffused light (which is the majority of the input light).

When viewed from above and lit from the side though, the majority of the light will reflect right off the surface, according to Fresnel! Only a very small fraction will be refracted, which is then diffused as above. The overhead camera won't receive any of the reflected light (which is the majority of the input), and instead only receives a small percentage of the diffused light (which itself is a small percentage of the input).

Have I thought about this all wrong? Or does reciprocity really break down when diffusers and Fresnel's laws are combined?

Actually, it's a lot easier to convert it to anisotropic than that.

Wow, thanks! I notice that the math for that distribution is exactly equal to your previous GGX distribution when the two roughness parameters are equal too... does the original GGX paper define this aniso version?

I'm still going to need some kind of retro-reflection hack (or, alternative physical BRDF) in my game so I can boost the effect right up for certain bits of paint and signage and... actual retro-reflector devices (like you put on your bicycle). You're right that there is a bit inherently in this BRDF, but it's mostly only at a grazing angle which is lost to N.L.
A macro-scale retro-reflector like you put on your bike -- a collection of 45º angled "V" shaped mirrored facets -- will direct almost all of the incoming light back towards the incident ray when lit from overhead, but performs worse at glancing angles, and it's this kind of behaviour that I'd ideally like to be able to model.

Also, Chris_F, be careful of this:

On that note, BRDF explorer's files spell "Ashikhmin" as "Ashikhman", and it's infecting me

### #3Hodgman

Posted 25 February 2013 - 07:25 PM

I might be getting a bit off topic now... forgive me

I went to bed last night with Helmholtz reciprocity on my mind -- apparently our physically based BRDF's should all obey this law, that if you swap a light source and a camera, you'll measure the same ray of light in either configuration, or in the case of our BRDF's, swapping L and V has no effect.

The thought experiment that caused me lost sleep was an optically-flat Lambertian diffuse plane (i.e. all microfacets are aligned with the normal, all refracted light is uniformly dispersed over the upper hemisphere), with the two observation/lighting angles being directly overhead (0º from the normal) and very nearly perpendicular (~90º).

When lit from above and viewed from the side, the majority of the light will be refracted into the surface and then diffused -- no matter where the camera is in the hemisphere, the surface will appear the same. The camera will receive a small percentage of the diffused light (which is the majority of the input light).

When viewed from above and lit from the side though, the majority of the light will reflect right off the surface, according to Fresnel! Only a very small fraction will be refracted, which is then diffused as above. The overhead camera won't receive any of the reflected light (which is the majority of the input), and instead only receives a small percentage of the diffused light (which itself is a small percentage of the input).

Have I thought about this all wrong? Or does reciprocity really break down when diffusers and Fresnel's laws are combined?

Actually, it's a lot easier to convert it to anisotropic than that.

Wow, thanks! I notice that the math for that distribution is exactly equal to your previous GGX distribution when the two roughness parameters are equal too... does the original GGX paper define this aniso version?

I'm still going to need some kind of retro-reflection hack in my game so I can boost the effect right up for certain bits of paint and signage. You're right that there is a bit inherently in this BRDF, but it's mostly only at a grazing angle which is lost to N.L.
A macro-scale retro-reflector -- a collection of 45º angled "V" shaped mirrored macro-facets -- will direct almost all of the incoming light back towards the incident ray when lit from overhead, but performs worse at glancing angles, and it's this kind of behaviour that I'd ideally like to be able to model.

Also, Chris_F, be careful of this:

On that note, BRDF explorer's files spell "Ashikhmin" as "Ashikhman", and it's infecting me

### #2Hodgman

Posted 25 February 2013 - 07:22 PM

I might be getting a bit off topic now... forgive me

I went to bed last night with Helmholtz reciprocity on my mind -- apparently our physically based BRDF's should all obey this law, that if you swap a light source and a camera, you'll measure the same ray of light in either configuration.

The thought experiment that caused me lost sleep was an optically-flat Lambertian diffuse plane (i.e. all microfacets are aligned with the normal, all refracted light is uniformly dispersed over the upper hemisphere), with the two observation/lighting angles being directly overhead (0º from the normal) and very nearly perpendicular (~90º).

When lit from above and viewed from the side, the majority of the light will be refracted into the surface and then diffused -- no matter where the camera is in the hemisphere, the surface will appear the same. The camera will receive a small percentage of the diffused light (which is the majority of the input light).

When viewed from above and lit from the side though, the majority of the light will reflect right off the surface, according to Fresnel! Only a very small fraction will be refracted, which is then diffused as above. The overhead camera won't receive any of the reflected light (which is the majority of the input), and instead only receives a small percentage of the diffused light (which itself is a small percentage of the input).

Have I thought about this all wrong? Or does reciprocity really break down when diffusers and Fresnel's laws are combined?

Actually, it's a lot easier to convert it to anisotropic than that.

Wow, thanks! I notice that the math for that distribution is exactly equal to your previous GGX distribution when the two roughness parameters are equal too... does the original GGX paper define this aniso version?

I'm still going to need some kind of retro-reflection hack in my game so I can boost the effect right up for certain bits of paint and signage. You're right that there is a bit inherently in this BRDF, but it's mostly only at a grazing angle which is lost to N.L.
A macro-scale retro-reflector -- a collection of 45º angled "V" shaped mirrored macro-facets -- will direct almost all of the incoming light back towards the incident ray when lit from overhead, but performs worse at glancing angles, and it's this kind of behaviour that I'd ideally like to be able to model.

Also, Chris_F, be careful of this:

On that note, BRDF explorer's files spell "Ashikhmin" as "Ashikhman", and it's infecting me

### #1Hodgman

Posted 25 February 2013 - 07:21 PM

I might be getting a bit off topic now... forgive me

I went to bed last night with Helmholtz reciprocity on my mind -- apparently our physically based BRDF's should all obey this law, that if you swap a light source and a camera, you'll measure the same ray of light in either configuration.

The thought experiment that caused me lost sleep was an optically-flat Lambertian diffuse plane (i.e. all microfacets are aligned with the normal, all refracted light is uniformly dispersed over the upper hemisphere), with the two observation/lighting angles being directly overhead (0º from the normal) and very nearly perpendicular (~90º).

When lit from above and viewed from the side, the majority of the light will be refracted into the surface and then diffused -- no matter where the camera is in the hemisphere, the surface will appear the same. The camera will receive a small percentage of the diffused light (which is the majority of the input light).

When viewed from above and lit from the side though, the majority of the light will reflect right off the surface, according to Fresnel! Only a very small fraction will be refracted, which is then diffused as above. The overhead camera won't receive any of the reflected light (which is the majority of the input), and instead only receives a small percentage of the diffused light (which itself is a small percentage of the input).

Have I thought about this all wrong? Or does reciprocity really break down when diffusers and Fresnel's laws are combined?

Actually, it's a lot easier to convert it to anisotropic than that.

Wow, thanks! I notice that the math for that distribution is exactly equal to your previous GGX distribution when the two roughness parameters are equal too... does the original GGX paper define this aniso version?

I'm still going to need some kind of retro-reflection hack in my game so I can boost the effect right up for certain bits of paint and signage. You're right that there is a bit inherently in this BRDF, but it's mostly only at a grazing angle which is lost to N.L.

A macro-scale retro-reflector -- a collection of 45º angled "V" shaped mirrored macro-facets -- will direct almost all of the incoming light back towards the incident ray when lit from overhead, but performs worse at glancing angles.

Also, Chris_F, be careful of this:

On that note, BRDF explorer's files spell Ashikhmin as Ashikhman, and it's infecting me

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