 Okay, so we have these two guys in the ring and we know already how to solve the illumination equation. The illumination equation. We don't measure radians, we measure intensity. It's not really unit and physics. It's just some heck-doth thing that happens to work. In the rendering equation, we measure radians and we have to do some kind of integration and this is, if you, the more you think about it, the more you possibly will sound to even the thought of solving this problem. So the first question is what can I earn by solving this equation? Because I have to be motivated to do it. So obviously, the result better be, better look really good in order to give me the motivation and the resources to solve it. So this is an image from the first assignment and this we have computed with recursive ray tracing. So you can see for instance, hard shadows. You can see that this is a reasonably boring image. I mean, it's great compared to the simplicity of the model that we have, but it's not really the greatest. Well, what is missing? Let's take a look and look very closely. Let's take a look at the very same scene, but not with recursive ray tracing, but with low-dolumination algorithms. So not the elimination equation, but the full rendering equation. Take a look at the difference. Look closely. This is full global illumination. Finally, absolutely beautiful. Let's take another look. This is recursive ray tracing and global illumination. So apparently there are some effects that recursive ray tracing cannot account for. What are these effects? Well, we have talked about indirect illumination or color reading. This is the very same thing. This means that I am hitting two diffuse objects, one after each other. Is this visible enough? Okay, I'm just pulling a bit on these pertains. So you guys can see better. Okay, perhaps a bit better, right? Yes. You're back. So these are in this case LEDV paths. What does it mean? Everyone knows you start out from the light source. You hit two diffuse objects and you hit the eye. Excellent. Now, indirect illumination is all around us everywhere. Both in the real world and both in the better computer games out there, which have approximations of indirect illumination. And you can see that on the left image, it almost looks like Photoshop. It is completely alien from its surroundings. It is almost as if it didn't take into consideration its surroundings. So you're standing in the middle of the desert, not just somewhere. You would have to have some color reading effect that you get from your surroundings. And this is what usually the problem is with many of the Photoshop images. You just repel the person from somewhere and you put it in another photograph and it looks super fake. And yes, mostly because of the illumination conditions, but even if you try to account for that, even if you try to recolor it to have more of that the same color scheme than the rest of the photograph. You're still missing the indirect illumination effect. And human eye is very keen in recognizing that. So you recognize that something is wrong, but you don't know what exactly is missing. And it's usually in the direct illumination. But there's something else. Let's take a look at this scene with recursive ray tracing. So we have refractive materials. For instance, this last sphere on the left of the mirror sphere in the middle and the completely diffuse sphere on the right. Let's take a look at how the very same scene looks like with global illumination. This is the difference. One more time. Recursive ray tracing and global illumination. So like we have talked about this before, I can see that difference is in indirect illumination. So on the upper left, I can see that some of the red color is bleeding onto the other wall and the very same with the green wall in the background. Also with this diffuse ball. So even a simple diffuse sphere looks much more interesting and much more beautiful with global illumination. Don't say anything. But I say something else. I see something else as well. Not only indirect illumination. I see some other effect on this image that I couldn't compute with ray tracing before. Don't say anything. Raise your hand if you know what I'm talking about. Excellent. How was that? Everyone. And what? Don't say anything. Okay. I'm talking about this. And this. So this interesting light effect on the wall and below this glass sphere. So raise your hand again if you know what this is exactly. Don't say anything. Because so many people know you will have to say all of you at the same time after three. Got it? Okay. So everyone. One. Two. Three. What is this? Just a little. Okay. What are the other guesses? That's technically a fraction. Yes. But that's not how we call the effect. Anyone else? Okay. This is what we call caustics. So what kind of light path is this? This is an interesting light path. In this case, this is L. S S D E Y because we start out from the light source. We hit the glass sphere from the outside. Then we have refraction. We hit it from the inside. And then we hit some diffuse object that is either this checker board down there or the red wall on the left. And then to the eye. And if we have this effect, then we are going to have caustics. It's a beautiful, beautiful phenomenon in nature that we can find the account for. And it's. And then you can you can see this many, many places. Now, let's take a look at another example. This is the famous school corridor example from Luxrender. Okay. We have recursive ray tracing and blue glid illumination. So you can see lots of indirect illumination. This reddish light on the floor and perhaps some caustics or at least caustic looking thing in front of the lovers. Okay. So next question. What is the definition of shadows again? So what we have said before that shadows are regions that are not visible from the light source. Now, an alternative definition of shadows is the absence of light. This is what definition we will use in group illumination. So there is you could say that there's no such thing as shadows. There's no. That's that's not something that's just the absence of something else. If there is less light somewhere, then there's going to be shadows. So this is the definition of shadows in local illumination and in Zen culture. And take a look at this image. We can see some beautiful, beautiful soft shadows. And the thing is that you don't even need to do anything to compute these illumination. So if I have a ray tracer, what do I do? I shoot out shadow rays from these regions and I try to approximate what regions of the light source are visible from this point. In global illumination, you don't need to do anything. You just solve this equation and outcomes, physical reality. And shadows are parts of physical reality. You don't need to do anything in order to obtain shadows. It's not like a bottom-up approach like ray tracing. So you start from a baseline and you add more and more hacks to account for more and more effects. And for global illumination, you will see that we will have a simple algorithm. That can give you all of this. And you don't need to account for shadows and costics and all of these things. Another beautiful example of costics. This is costics from the point light source because, for instance, you can take a look at the shadows. The shadows are hard. So it's likely to be a small or a point light source. And the costics are very sharp. So they have the same behavior to large light sources as shadows. And another beauty with costics. Okay, so let's assess what these recursive ray facers are capable of doing and what they cannot. Well, obviously they cannot compute indirect illumination. Indirect illumination means two diffuse bounces or possibly more. This you cannot compute correctly. We will talk about why. And you cannot compute costics. Well, costics I have written in a few scenes ago that it was LSSD. So two specular bounces and that they do because you have to go through the blastbox. And here I'm writing something completely different. I just say one specular bounce is necessary, the rest are optional. Is this true? Or how can we verify this is true? In order to find out if this is true or not, I don't even need to say a word. I can just do this. You see the costics? This is one of the costics inside. Can you two see it? Yes. Excellent. Please take a look. No one still exists my writing name. My fiance is going to kill me. Okay, you two have seen it. Okay. Okay. Okay. Nice. Beautiful. I was going to say I'm going to put it in the bin. Okay. So apparently rings have costics. Well, I start off from the light source. I think one specular object, one mirror light object and then a diffuse which is the table and then the I have costics. So LSSD is enough for costics. There's no need to prove it in any other way. Just take a look at physical reality and let it be your touch always.