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14 votes
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How to properly combine the diffuse and specular terms?

Using two Fresnel terms is correct in the sense that any given diffuse path will pass through the surface twice. If you're solving diffusion by tracing a path through the medium until it bounces out ...
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12 votes
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What explains the high specularity of metals?

Warning: I am not a physicist. As Dan Hulme already explained, light can't travel through metals, so dealing with IOR is a lot more... complex. I will answer why that happens and how to calculate the ...
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9 votes
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In a physically based BRDF, what vector should be used to compute the Fresnel coefficient?

In Schlick's 1994 paper, "An Inexpensive Model for Physically-Based Rendering", where they derive the approximation, the formula is: $$F_{\lambda}(u) = f_{\lambda} + (1 - f_{\lambda})(1 - u)^...
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  • 3,552
8 votes

In a physically based BRDF, what vector should be used to compute the Fresnel coefficient?

The Fresnel coefficient should be evaluated using $H$, not $N$. You wrote, I have trouble seeing why we can still use that formula in a BRDF, which is supposed to approximate the integral over all ...
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8 votes

How to properly combine the diffuse and specular terms?

While browsing to properly write my question, I actually found the answer, which happens to be very simple. Another Fresnel term is also going to weight in as the photons make their way out of the ...
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6 votes
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Fresnel and specular colour

Yes, because refractive index can vary with wavelength. This is the origin of colored specular reflection in metals such as gold and copper; most other materials have essentially uncolored specular. ...
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6 votes

What explains the high specularity of metals?

Look at the refractive index of several metals. They are all complex numbers and the math does work out when you put this into the fresnel equation: you get the expected high reflectivity at all ...
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  • 1,575
6 votes
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Why is the half vector not used in diffuse BRDF Fresnel calculations?

I finally figured out a flaw in my argumentation to use the half vector for the diffuse part. tl;dr version: $\alpha_{hi}$ and $\alpha_{ho}$ are not equal, this assumption only works for the specular ...
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  • 1,457
6 votes
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Fresnel equation with incident angle, n and k as input

@PaulHK's answer is correct I'm sure, here's a bit of a check to show that the IOR() function is calculating the reflection coefficients for $s$ and $p$ ...
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  • 330
5 votes
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"Artist Friendly Metallic Fresnel" reversible?

I wasn't really expecting that, no. The formula in the paper is not the most elegant - there's quite a few parentheses in there. In this case I think it's just a matter of shuffling the parentheses ...
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  • 66
4 votes

Fresnel equation with incident angle, n and k as input

This is the complex number version of refraction, were K is the extinction coefficient. This is commonly used for metals. You can check the Wikipedia on refraction: Complex refractive index | ...
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3 votes
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Iridescence/Thin-film interference integration as a layer

Unfortunately, the iridescence model is not made to be applied to a diffuse term. Pascal and I made it for microfacet models only (that is the specular term). One way to understand how to include it ...
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2 votes

What explains the high specularity of metals?

The refractive index is related to the speed at which light travels through the medium, and only applies to materials which are at least partially transparent. Metals are electrically conductive, so ...
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  • 6,490
2 votes

More accurate Fresnel approximation for a RGB-based Path Tracer

This would be a response to why is it possible to use the Fresnel equations in an RGB path tracer. Though evaluating Fresnel equation directly requires some what more information about the environment ...
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  • 441
2 votes

Equivalent of Fresnel law for determining transmitted/diffuse split

Physically, the origin of diffuse light is subsurface scattering, which happens continuously as light travels through a material. So, the proportion of transmitted light depends on the thickness of ...
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2 votes

Why is the half vector not used in diffuse BRDF Fresnel calculations?

We're actually going through that paper for our own GGX BRDF metallic & edge_tint model, and we've spotted one crucial problem. Hammon is still using the Fresnel Schlick approximation for his ...
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  • 21
1 vote

BRDF sampling and evaluation of diffuse vs specular component

So I found a solution on a shader toy. I choose randomly from sampling diffuse or sampling specular with distribution 50:50. But I calculate PDF of both and average then. If you want to use a ...
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1 vote
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Correct way to think about Fresnel effect

If you just implement Fresnel alone you'll see that what you think in your original question is mainly correct for dieletric materials. However don't calculate Fresnel ahead and then stochastically ...
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1 vote

Correct way to think about Fresnel effect

BIG UPDATE and explanation of BRDF model While I was cleaning my browser and closing about 100 tabs I found this awesome website (it was there 3 days so I could already found an answer...) which ...
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1 vote

Correct way to think about Fresnel effect

I will answer based on my experience with Fresnel models. Due to Kirchhoff's law of thermal radiation, in an opaque material the emissivity plus reflectivity plus absorptivity equals to one for every ...
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  • 111
1 vote
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Confused on reflection coeffcient of Fresnel equations

We have $t_{12} = t_{21}$, by the law of reciprocity. Also, $$r_{12} + t_{12} = 1\\r_{21} + t_{21} = 1$$ It follows that $r_{12} = r_{21}$ as well.
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