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4 replies to this topic

### #1Chris_F  Members

Posted 31 January 2013 - 10:20 PM

What's the best way to go about geting realistic metals? I haven't seen it mentioned much. Currenly I am calculating my frenel term as a float3 with schlick's approximation, and different zero incident values based on the reflectance values you can get from here: (http://refractiveindex.info/)

Is this a close enough approximation? Are there better ways of handeling it? The colors seem about right to me, and the specular highlight turns white at glancing angles which seems right.

### #2Frenetic Pony  Members

Posted 31 January 2013 - 10:41 PM

Depends on how much work you want to go into, and your target platforms.

Good enough can be, well, good enough. As long as it's handled is all specular/no diffuse, it can look fine. But if you really wanted to get something better you could apply a better BRDF that handles reproducing metallic materials better, take a look at his stuff:

http://www.cs.cornell.edu/~srm/publications/EGSR07-btdf.pdf

### #3CryZe  Members

Posted 01 February 2013 - 02:07 AM

Oh wait, you want to do metals with the fresnel equations? If that's the case, your formula from the other thread won't work. Metals usually have complex reflective indices (complex numbers). Fresnel's equations work with complex numbers though, your implementation just doesn't. You need complex multiplication, complex addition and the absolute value (which you didn't implement) needs to work with complex numbers as well. Also since metals have chromatic reflections you would have to calculate your fresnel term for all 3 color channels. I'd use Schlick's approximation, reduce most of it to constant time, and reduce other parts of the formula to scalar calculations, while only the necessary parts get calculated for all color channels.

Here's approximately how that code should look like. You should probably calculate the constant part per vertex or per draw call on the CPU, if possible:

float2 f0CmplxRed = cmplxDiv(cmplxSub(n1Red, n2Red), cmplxAdd(n1Red, n2Red));
float2 f0CmplxGreen = cmplxDiv(cmplxSub(n1Green, n2Green), cmplxAdd(n1Green, n2Green));
float2 f0CmplxBlue = cmplxDiv(cmplxSub(n1Blue, n2Blue), cmplxAdd(n1Blue, n2Blue));

float3 f0Sqrt = 0;
f0Sqrt.r = cmplxAbs(f0CmplxRed);
f0Sqrt.g = cmplxAbs(f0CmplxGreen);
f0Sqrt.b = cmplxAbs(f0CmplxBlue);

float3 f0 = f0Sqrt * f0Sqrt;
float3 cf0 = 1 - f0;

foreach (light)
{
float factor = pow(1 - dot(L, H), 5);
float3 fresnel = f0 + cf0 * factor;
}


### #4Chris_F  Members

Posted 01 February 2013 - 03:50 AM

Oh wait, you want to do metals with the fresnel equations? If that's the case, your formula from the other thread won't work. Metals usually have complex reflective indices (complex numbers). Fresnel's equations work with complex numbers though, your implementation just doesn't. You need complex multiplication, complex addition and the absolute value (which you didn't implement) needs to work with complex numbers as well. Also since metals have chromatic reflections you would have to calculate your fresnel term for all 3 color channels. I'd use Schlick's approximation, reduce most of it to constant time, and reduce other parts of the formula to scalar calculations, while only the necessary parts get calculated for all color channels.

Here's approximately how that code should look like. You should probably calculate the constant part per vertex or per draw call on the CPU, if possible:

float2 f0CmplxRed = cmplxDiv(cmplxSub(n1Red, n2Red), cmplxAdd(n1Red, n2Red));
float2 f0CmplxGreen = cmplxDiv(cmplxSub(n1Green, n2Green), cmplxAdd(n1Green, n2Green));
float2 f0CmplxBlue = cmplxDiv(cmplxSub(n1Blue, n2Blue), cmplxAdd(n1Blue, n2Blue));

float3 f0Sqrt = 0;
f0Sqrt.r = cmplxAbs(f0CmplxRed);
f0Sqrt.g = cmplxAbs(f0CmplxGreen);
f0Sqrt.b = cmplxAbs(f0CmplxBlue);

float3 f0 = f0Sqrt * f0Sqrt;
float3 cf0 = 1 - f0;

foreach (light)
{
float factor = pow(1 - dot(L, H), 5);
float3 fresnel = f0 + cf0 * factor;
}


But the complex number math is only nesisarry to get the zero incident reflection value from the complex IOR. The website I linked not only lists the complex IORs, but also the reflectance values for arbitrary wavelengths at arbitrary incidents, so I can simply input the f0 values into the shader as a constant for my material or from a texture map. No need to work in term of IOR. I just wanted to know if calculating the reflectance coeficient for just R, G and B was a close enough aproximation to get realistic metal specular reflections.

### #5CryZe  Members

Posted 01 February 2013 - 04:17 AM

he website I linked not only lists the complex IORs, but also the reflectance values for arbitrary wavelengths at arbitrary incidents

I know this website, I've used it quite some time before

so I can simply input the f0 values into the shader as a constant for my material or from a texture map. No need to work in term of IOR.

I just wanted to let you know, that you need to work with all the 3 channels and the complex numbers. Like I said, you could do it per pixel, per vertex or per draw call on the CPU and simply input f0 and maybe also cf0 into the shader as constants. It depends on where you get your values. If n2Red, n2Green, n2Blue would be stored in a texture, you would have to do it per pixel, or you bake your f0 values into a texture and use the baked texture instead. But if you can do it per draw call, go ahead and calculate it on the cpu.

I just wanted to know if calculating the reflectance coeficient for just R, G and B was a close enough aproximation to get realistic metal specular reflections.

Yes, that should be enough. You should worry more about the microfacets though. Blinn-Phong is not such a good distribution term for metals and even more important is shadowing and masking of the microfacets: the geometry / visibility term.

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