Question on metals for vlado - anywhere to get the diffuse component to acompany ref?

[joconnell]

Hi Vlado,

Just as a quick one, I've found a method to take the fresnel equation for metals and loop through 0 to 90 degrees working out the reflection part using the real and imaginary values from refractiveindex.info but of course with metals not being 100% reflective, there's also a diffuse component. Do you know of any method or scale or system to work out what the diffuse colour would be to go along with them? And also assuming the info I have is correct as regards the percentage of reflection at each angle, I'd only really need the hue of the colour to be accurate with the energy preservation laws removing the majority of the diffuse contribution once the reflection is applied?

Cheers!

John

[anchovy]

Sounds like we need Cook-Torrance or Trowbridge-Reitz. At siggraph this year there was a great presentation from Disney, its worth taking a look.

http://disney-animation.s3.amazonaws..._slides_v2.pdf

-Michael

[joconnell]

More so a simple colour value in my case Michael! I can get a curve from scanned wavelength data for metals but I don't have an equivalent diffuse colour value to fill in the other part of the materials. It's a very simple thing by comparison but might be useful in some cases. Internet connection is like sludge here today but downloading that paper - cheers for the link!

[Morbid Angel]

Sounds like we need Cook-Torrance or Trowbridge-Reitz. At siggraph this year there was a great presentation from Disney, its worth taking a look.

http://disney-animation.s3.amazonaws..._slides_v2.pdf

-Michael

I love it...

[Rens]

For metals there basically is no different diffuse part in the sense that the top layer reflects pretty much everything. This is different in dielectrics where the reflection part is 'uncoloured' and the diffuse part is 'coloured'.
So for metals you can roughly take the average of the gradient and plug that in the diffuse colour of a different shader and blend the two materials.


If you want to be more exact; the angles of the outgoing rays vary more the rougher the surface gets. They fan out around the angle that the outgoing ray would have if the surface would be perfectly smooth.
Imagine the surface consisting of small facets. On a perfectly smooth surface the facets align with the surface normal. When the surface gets rougher the facets rotate around that normal.

Say for example that the facets can rotate between 0 (surface normal) and, say, 90 degrees offset away from the axis.
Now, each surface has a different distribution of angles. If the outgoing angles would be perfectly random, you'd get a lambertian surface. That in VRay is your diffuse part.
All angles at 0 degrees offset would be the reflection part without any glossiness applied.
If all would be at 30 degrees it would roughly be reflection at a certain glossiness amount.

However the distribution on surfaces is usually very different. For example you could have a surface with 10% at 0 degrees, 12% at 10 degrees, 15% at 20 degrees, etc. It's a distribution curve, not a single value.
So you could have a smooth material with a strong specular highlight with a bigger softer 'glossy' highlight around it where the facets have a larget offset and then also a smaller more diffuse, less smooth part.
Unfortunately you can't do that in vray, unless you put together a whole lot of materials in a blend, or randomise the normals at rendertime with for instance a noisy normal map, or a very very fine glossiness map with tons of samples. All not very practical.
Note that mixing a pure diffuse material with a smooth reflection material results in a distribution curve which you'll probaly never see in real life, as basically it's all or nothing and nothing in between.

To be very exact you'd need the average of all the reflection amounts of all the 'facets' under a single pixel.


Another thing is that the reflection amount is multiplied on top of the reflected color (the environment). So when you get your gradient (using complex numbers I hope!) and drive it with a falloff it just gets multiplied on top, regardless of the current glossiness setting. Basically the rougher the surface (lower glossiness setting) the more varied the angle. But you'd still see the edges of the object have 100% reflection amount regardless of glossiness setting. Theoretically this edge would need to blur out at least a bit as the surface gets rougher.


Just the correct hue for the diffuse won't do it though as you'd need the value as well, in nature there is practically speaking no difference between diffuse and reflection in metals and in dielectrics it's the subsurface and surface respectively.
Also, don't put the diffuse colour and reflection colour in the same material as that will give you a wrong output. The vrayMtl is not made for metals if you want a diffuse part as well. The shader leaves the difference between white and the reflection colour for the diffuse part. This is fine for uncoloured reflections in dielectrics, but for metal reflections this would result in a very tinted diffuse part as it gets multiplied with the leftovers from the reflection, which is wrong as it is technically also part of the reflection.
Best would be a non-additive blend amount between the two. One shader diffuse, the second shader reflection. The diffuse filter should roughly be the average of the reflection filter for each separate material, only when you mix the materials should the values change, but still add up to the (average) reflection amount.
Make a vrayMtl with an orange colour in both the diffuse and reflection, and then make a blend material with one material just orange diffuse and the other material just orange reflection, rest black. The single material will look green, which is wrong for a metal.


Also, for the gradient you'll need to calculate the reflection amount not only at all angles but at each R, G and B wavelength as well, so you get a coloured gradient. This is because different wavelengths reflect different amounts, and is why gold has a warm tint to it.


Actually it would be nice to have a VRay shader for metals, which has an adjustable internal calculated gradient so it doesn't have to do complex number fresnel calculations at render time, which has the ability to roughen the surface according to a distribution curve, maybe a 2D one for anisotropic materials, and which blends the Lambertian and ray-traced parts correctly if you'd have the need for a diffuse part.

[joconnell]

Best would be a non-additive blend amount between the two. One shader diffuse, the second shader reflection. The diffuse filter should roughly be the average of the reflection filter for each separate material, only when you mix the materials should the values change, but still add up to the (average) reflection amount.
Make a vrayMtl with an orange colour in both the diffuse and reflection, and then make a blend material with one material just orange diffuse and the other material just orange reflection, rest black. The single material will look green, which is wrong for a metal.

Cheers for the pointer on hue / diffuse as a faceting issue - so essentially what you're saying is it's polish that's determining it?

I understand what you're getting at here since the orange reflection will bounce off orange parts of the light spectrum and only allow the other parts to hit the diffuse section of the surface, hence the green diffuse only showing afterwards. In terms of the diffuse filter you mention here are you saying to calculate the average luminance of the reflection curve and use this as the curve that blends between the two materials? It makes sense since you're preventing that tinting by product of trying to do everything in one material, but does it not knock down the strength of the reflections as a result? As in all of the scan data that give me my curves have taken into account the intensity of the reflections on the surface already (lets say it's 0.9, 0.91, 0.89 reflective at 0 degrees), so by working out another curve with the average luminance of this curve (0.9) and using it to blend the reflection over a diffuse material you're knocking down the strength of the reflections roughly twice and breaking the connection between our scanned reflection data in terms of correct intensity (correct being a loose term since the scan data came from one pure single unique source, thus isn't a rule for all other sources) and our vray approximation. Or rather than making a second custom gradient for your luma intensity blend from 0 - 90 degrees are you talking about having a single simple luma value and just using the colour swatch on the vray blend to lay the reflections over the surface?

Also, for the gradient you'll need to calculate the reflection amount not only at all angles but at each R, G and B wavelength as well, so you get a coloured gradient. This is because different wavelengths reflect different amounts, and is why gold has a warm tint to it.

Yep - all being done from three wavelength's real and imaginary parts so it is giving me coloured values for each curve, even if some tend towards something quite desaturated.

[Rens]

Cheers for the pointer on hue / diffuse as a faceting issue - so essentially what you're saying is it's polish that's determining it?

Polish or surface roughness determines the scattering of the rays. A perfectly smooth surface has no scattering, a 'glossy' surface has some, and a diffuse lambertian surface has perfect scattering.

I understand what you're getting at here since the orange reflection will bounce off orange parts of the light spectrum and only allow the other parts to hit the diffuse section of the surface, hence the green diffuse only showing afterwards. In terms of the diffuse filter you mention here are you saying to calculate the average luminance of the reflection curve and use this as the curve that blends between the two materials? It makes sense since you're preventing that tinting by product of trying to do everything in one material, but does it not knock down the strength of the reflections as a result? As in all of the scan data that give me my curves have taken into account the intensity of the reflections on the surface already (lets say it's 0.9, 0.91, 0.89 reflective at 0 degrees), so by working out another curve with the average luminance of this curve (0.9) and using it to blend the reflection over a diffuse material you're knocking down the strength of the reflections roughly twice and breaking the connection between our scanned reflection data in terms of correct intensity (correct being a loose term since the scan data came from one pure single unique source, thus isn't a rule for all other sources) and our vray approximation. Or rather than making a second custom gradient for your luma intensity blend from 0 - 90 degrees are you talking about having a single simple luma value and just using the colour swatch on the vray blend to lay the reflections over the surface?

So basically for shading purposes metal doesn't have a sub-surface. However, you could make the surface so rough that it would come close to a Lambertian surface.
In that case, the gradient you made still applies, but it gets smoothed out because all the different angles along the gradient get mixed up, blurred together. For a material with just a diffuse colour like this, it would be the average of all the angles.
If on your 0 degrees you have [0.9, 0.91, 0.89] and at 90 degrees you have [1.0, 1.0, 1.0] you'd end up with a single RGB value (closer to the RGB value at 0 degrees than 90 degrees because it ramps up).
However, the R, G and B values will still be different from each other.
So for gold you'll still end up with a warm colour: [0.95, 0.74, 0.47]
This is all the angles blended together, not all the values blended together.
The value or luma or reflection amount is already in the colour, as it's just the reflection amount of the three wavelengths, and the diffuse colour is just the average of the colours at all the angles between 0 and 90 in the curve. The Average Blur filter in Photoshop will do the trick.

Then you basically blend between the same metal, but with different surface roughnesses. Even if one has the colour in the diffuse and the other in the reflection. One is just perfectly rough and the other not.

Note however, as a diffuse material doesn't use raytracing that you will need GI to get to the same amount of lighting, or energy hitting the material.

Shader names are very confusing when comparing them to their real-world counterparts.

Yep - all being done from three wavelength's real and imaginary parts so it is giving me coloured values for each curve, even if some tend towards something quite desaturated.

Nice! Yeah it usually does seem desaturated though.

[joconnell]

Ah I get you now, so the scan data is setting the top limit of the amount of light than can come back from the surface whether more diffuse or more reflective, so I can in theory use a totally reflective version of the material, a more glossy version and a base diffuse layer, and then just use simple grey colour swatches in the blend material to determine how focused or polished my metal is?

[Rens]

Correct!

----

[joconnell]

Crackin - will send you over a mat library and a script so. One major annoyance is the built in gradient ramp in max doesn't have script options to create flags for it's colours so you have to start with a premade grad and then modify values. Bercon grad gets around this but not everyone has it. Aside from giving you a way of using that fresnel equation I also don't know if this'll offer any major benefit over doing a simple material by eye but what the hell

[Rens]

Hehe, well it will allow you to do a quick gradient from values you know (or a preset) and work from there. At least it will get the falloff to 100% reflective at grazing angles correct, which is trickier to get right by hand.

Yeah there's no way around that unfortunately. Also the Bercon Gradient will corrupt your scene if you use it inside the new Composite map, but it's really great though.
I have a similar script which will instead of tweaking an existing gradient will create a bitmap that you can then drive with a falloff. Though I can't remember exactly how I set it up for max, I think I set a Gradient Ramp to mapped, dropped a falloff map in there and then dropped the calculated gradient tex in the two keys, something like that.

[joconnell]

Just popping you something over - it's set to work on that gradient in map slot one of the material editor and there's zero error checking but see if it's any use! Max 2012 scene and a maxscript.

[Rens]

Contrary to what I said before the VRayMtl works fine for coloured reflections if you use the monochrome energy preservation mode, which makes sense. (Thanks for pointing that out Lele)