# OpenGL BRDFs in shaders

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I'm reading a book called Real Time Rendering (3rd edition) and the author expresses the BRDF function for non-area light sources:

1. What's the difference between irradiance and radiance? English isn't my first language and dictionaries fail me.

2. "... is the irradiance of a light source measured in a plane perpendicular to the light direction vector l" can someone explain this? How can a light quantity be measued in a plane?

3. I followed basic OpenGL books and tutorials and I never worked with these kind of stuff. Radiance and irradiance were never introduced in the shaders. Is this concept really needed?

Edited by Pilpel

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Thanks for the explanation. I'm so mad. This chapter is absolutely cancer.

Do you know any source that explains BRDFs better than this book? All I care about is shader code, really..

Edited by Pilpel

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If I had to recommend one book it'd probably be PBRT (click). If you just care about shader code you might aswell google for that. Plenty of code out there. Most notably the Unreal Engine 4 source code on GitHub (click).

My two cents about this: I remember spotting a bug in the PDF for their BRDF in their codebase so trying to decipher the math by looking at code is probably not the best way to tackle this. People make mistakes. Programmers make a lot of mistakes. The chance of running into something you don't understand simply because there's a mistake in there is much higher than for stuff that was written down on paper.

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All I care about is shader code, really..

I take that back, I was really mad.

I did, however, give up on the explanations from Real-Time Rendering. They are really hard for me to understand.

Also, it seems like the author was explaining PBR without saying it was PBR..?

I'm looking for better (easier) explanations about this topic, rather than the book yoshi_t mentioned. Any idea?

Edited by Pilpel

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All I care about is shader code, really..

I take that back, I was really mad.

I did, however, give up on the explanations from Real-Time Rendering. They are really hard for me to understand.

Also, it seems like the author was explaining PBR without saying it was PBR..?

I'm looking for better (easier) explanations about this topic, rather than the book yoshi_t mentioned. Any idea?

As a piece of advice, it might be better to work through the hard stuff if you want to understand BRDFs and PBR. You're going to hit a point where there's no way around the math and radiometry theory, and you're going to hit it fast.

You're entering a realm of graphics where there's no more training wheels, better get used to it sooner rather than later.

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I'm looking for better (easier) explanations about this topic, rather than the book yoshi_t mentioned. Any idea?

okay let's see....

Irradiance is the quantity of energy that is measured on a surface location incoming from all directions (that is mostly shown in literature as the letter E)

Now you may be confused and say "But hey if irradiance (E) is measured on a single location what's E_L then aka the irradiance measured on a surface perpendicular to L".

The irradiance perpendicular to L (E_L) is the amount of energy passing through a unit sized plane (don't get confused by this it's just something to make the measuring easier). You can think of it as the amount of energy the light source itself emits. Think of a light bulb emitting light with some amount of intensity into a direction. That is your E_L.

Radiance on the other hand is basically the same as irradiance (also remember radiance can be incoming or outgoing energy!) but not from all directions but only a limited or focused amount (think of a camera lens focusing light into a small amount of directions, that is the solid angle).

In the equation above it shows outgoing radiance (L_o) which is light reflecting from your surface location into a certain amount of directions.

I hope that is somewhat easier to understand...if it's still a little too hard to grasp here's the short version:

1. Irradiance = light energy on a single location from all incoming directions

?    ?Radiance = light energy on a single location from a small set of directions (solid angle)

Solid Angle = small set of directions in 3D space (think of a piece of cake)

2. Irradiance measured on a plane perpendicular to the light direction = light flowing through a unit sized plane (for measurement sake) to basically tell you how much energy the light is emitting/transmitting

3. Pretty sure if you've done anything that involves light or texture color you've made use of those equations (even if you didn't know).

Radiometry is just a way to mathematically or physically explain / define those things

The problem with radiometry is often that the "basics" are confusing since they are already based on simplification or approximations of more advanced equations.

Maybe try to keep going and see if it starts to make more sense going further...

For example later on when they explain how irradiance is obtained by summing up incoming radiance over all directions it made more sense to me

Edited by lipsryme

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Thanks a lot!

I went back to the basics and I'm not sure if I understand the difference between E and E_L.

E is irradiance from all directions onto a (unit?) plane. E_L is irradiance onto a plane, when only measuring light from direction L?

Edited by Pilpel

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E is the irradiance measured on a surface location (in your shading that would be the pixel you shade on your geometry).

E_L is irradiance measured not on a surface location but on a unit plane. The L subscript tells you already that it is irradiance corresponding to the light source.

edit: What you wrote is correct, although it's kind of confusing to think about shading a surface location as measuring it on a plane. This plane is kind of imaginary but perpendicular to the normal vector at that location, hence the N dot L term is born to saturate the amount of light depending on the angle the light hits this plane.

Here are a few quotes from RealTimeRendering:

- "The emission of a directional light source can be quantified by measuring power through a unit area surface perpendicular to L. This quantity, called irradiance, is equivalent to the sum of energies of the photons passing through the surface in one second".

Note: He's talking about E_L here, irradiance perpendicular to the light source L.

- "Although measuring irradiance at a plane perpendicular to L tells us how bright the light is in general, to compute its illumination on a surface, we need to measure irradiance at a plane parallel to that surface..."

Note: He goes on to talk about how the N dot L factor is derived...

On page 103 you can see that irradiance E is equal to the irradiance E_L times the cosine angle between the surface normal N and the light direction L.

E = E_L * cos_theta_i

looking at the equation in your original post it now makes sense because it now translates the brdf into:

aka the ratio between outgoing light into a small set of directions (in this case in the direction of our sensor/eye, which is vector V) and incoming light to this surface location (or rather a plane perpendicular to the surface normal N)

so finally to translate this into actual hlsl code your very simple light equation could look like this:

float3 E_L = light_intensity * light_color;
float cos_theta_i = saturate(dot(N, -L)); // negate L because we go from surface to light
float3 E = E_L * cos_theta_i;

// We actually output outgoing radiance here but since this is a very simplified/approximated BRDF
// we can set this equal since we assume that diffuse light is reflected the same in all directions
return E;


which is the lambertian shading / BRDF :)

Edited by lipsryme

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I finally get it. Thanks a lot

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