 How was the Easter break? With nice, too short. Come on. We discussed it already. But what would be an appropriate length? For it. It's a big day for this one. Bigger two weeks. Bigger weeks. Maybe the entire curriculum. Yes. And just extended every time that. So every time by just two more weeks or something. That's not new. Yeah. Well, I don't know about Austria, but in Hungary people usually go to their friends. You know, many people are coming over and we are hanging out with other people. And you always have to drink their stuff. So you go there and we have this drink that's called the Piling Cup. It's something like a snub, but way stronger. And I told this to some Austrian people and they were like, Oh my God, stronger than the slubs. How can that be? Very easily, at least the hundreds. So that's how it works. And you go to the very first place and you have to drink from there home room, old fool, Piling Cup. Usually it's very old fool. And you even have to say something to the about it. So you drink it, that is it. But you have to say something good about this because they are looking at you. What will be the reaction? So you say that it puts, that's really strong. And most people seem to be satisfied with that. So this is usually what I say. But then when you are at like the fifth station for 10 days, and some people just don't take no for an answer, unfortunately. So this is how it goes. Is it any better in Austria? It's more family politics. Okay. Okay, yeah, the family part is actually the nice part. So we can decide if we drink our own stuff or not. But I mean, my fiance's grandfather attempted to make some brew, some harlequat home. And well, he did something. Okay, so I mean, something was created in the process. But after tasting it, even the postman didn't want to drink it. I don't know about postman in Austria, but in Hungary they are really hardly people. So they drink whatever they find. Because obviously you don't give the good stuff for the postman. You give them the leftovers. It's like no one drank, oh, it's really good for the postman. And he's happy with that. Imagine that postman drank. Why are you doing postman? It's kind of weird here. Yeah, well, they are... They seem to like alcohol according to my experiences. And even the postman didn't want to drink that anymore. And next time we have seen him around the house. And he just came in front of the main door. And we wave to him, hey, come, we have some for you. No, no, no, I'm just going to put them in here. Immediately. Okay, so regarding the assignments, you guys and girls have done really well. So I'm very happy to see that. People realize that there is some exponentiality with respect to the depth of the city. And that's of the simulation. So the more people go, then the more exponential things become. But this is after like, I mean, it's exponential all along, but you don't know this because it starts off slow. But after like 10 to 15 bounces, you can see a very telling characteristic of this exponential distribution. And many of you have recognized correctly that this is because a reflection and reflection are sampled. All the time. So whenever I have a bounce, I am going to compute an intersection. And then there's going to be two rays, perhaps, that continue their way because one is going to be the reflection direction. And one is with reflection. And this quickly gets out of hand because wherever ray you have two more, that's the definition of something that is exponential. So well done. Let's proceed a bit and I'm going to talk just a bit about some advanced, a bit more advanced BRDF models that are mostly used with ray-tracing. So you remember this combustion BRDF that you see on the right. And this is the scalar product between L and then. So light factor and the normal. And obviously you can scale this with KD, which is some kind of diffuser video. Now if you put it next to a really image of the diffuser material, obviously it is a question, you know, what do we call the diffuser material? Or where was this for the BRDF? How exactly? But let's disregard this. And let's accept that we have this difference between the two. And if you take a good look, then it becomes apparent that in grazing angles, the simulated diffuser material seems to be completed on. And if you take a look at the formula up there, then this is a self-explanatory because the normal and the normal and the light direction can get perpendicular. And then you will see this darkness. So there are some advanced BRDF models that try to be a bit more realistic in this regard. Such example is the ORN-AIR model, which is much closer to what you would measure in real life. But let's note that all of these simplified BRDF models, these are all tags. This is not what physical reality is. People write up the actual equations that relate to physical reality and try to simplify in a way that a simple ray-facer can capture. We are going to talk about global effects and what a real diffused material looks like in a few minutes. So this ORN-AIR model seems much better. And what's even more, it can take into consideration these microscopic imperfections in different materials. And you can get a roughness parameter that can model these imperfections. What about specular models? Well, the form model, V.R, that we have talked about, is not the only way to do it. There is also the form-plane model, which is a more advanced model, and uses this H, this half vector between L and V. And it produces different results. I think this image is maybe not the best because yes, the highlights are different. One of the main advantages of this material model is that the shape of the specular reflections can get a bit more elliptic, depending on the viewing direction and the surroundings. So here you have the very same circular thing. So it's not the best example, but you can see that it's different. It looks more realistic. And we still have to think about the fact that these are still really good models. But these are still the X. There's also the Cooctorian model that's basically foam-plane. That can model also microscopic roughness. And here, maybe with the projector, maybe it's not so visible, but you can see that the specular reflection here is a bit more easier. So it's not a completely round sphere, it's not a perfect sphere, there are these small imperfections that are characteristic to viewing those materials. So this is what this model can capture. And there are some other advanced BRDF models, some of which are more easy to understand that implement that it is to pronounce the name of the authors of the BRDF models. This is one of those examples. And this is some kind of multilayer model where you have a diffused substrate and you have like a coating, a specular coating. So there are also BRDFs for car paint, where you can have these sparkly effects. And there are many BRDF models that capture given effects. Okay, what if one would like to play with these? The Disney guys have implemented this program called the BRDF Explorer. And you can load many local BRDF models and change the light source positions, look at the actual BRDFs and the impulse responses. Give it a try. So we have always been talking about cameras. So we are trying to model real world cameras. If you have an handheld camera, you will see a setting that's called the F-stop. And the F-stop is related to the size of the aperture. The aperture is the opening of the camera where the light goes in. And you can set this to different values. And you will notice that if you set this F-stop to a high value, then the aperture of the camera is going to become smaller. And if it's smaller, then this means that less light is left in. And more of the image that you get is going to be in focus. And vice versa. So if you have a low F-stop setting, then you will have a bigger aperture. More light is left in. And more regions will be out of focus. And what gives you this depth of field effect. Because whatever images we have seen and created with ray tracer yet, don't have this depth of field effect. But if you use a handheld camera, then somehow you have to model this effect as well. Because this is how an image will be created in a real world. So this is a nice chart made by Photograph First to see how exactly these F-stops will lead to an aperture size, what are the typical settings and all these interesting things. And an actual example. So let's take a look at the bottom right here. You can see that the whole image is in focus. And as you adjust the F-stop accordingly, you can see the top left. And see here immediately that the background is heavily blurred. So this is a more pronounced depth of field effect. It would be wonderful to have a ray tracer that can take this effect into account. And this is another maybe a bit more beautiful and a bit more visible example. So the left side you can see a very pronounced depth of field effect on the right. And it's close to everything is in focus. Yes. Do you also use the word OK for computer graphics? Yes. And there is also a bunch of papers on how to simulate this effect. So people even try to compute this in real time. So you have like a computer game, you would like to see this OK effect. How do you do this? And you have to take into consideration the depth. If you know what objects are wearing exactly how far away, then you can do a bunch of tricks. To get something like that in the approximation real time. And if you do this something that I'm going to show you in a second, then you will have the very same effect in your ray tracer from the left. Completely only focus image on the right. You can see again the depth of field effect, especially in the background. The further away you go, the more you see. So how do we do this? Very simple. Let's skip the text and I just put this here because people who read this at home would know about this. So mostly most of what we do is we shoot a ray through the midpoint of the pixel in our ray tracer. And this is going to touch this focal point and then hit an object. What we can do is that we would also take samples from nearby. So not only this pixel and not only the midpoint, but from nearby. And shoot all of these where is through the same focal point. And compute the very same samples, but these samples will be nearby. What we do with these samples is we average them. And this is what is going to give you this depth of field effect. So this is already some kind of integration. This means that, which if you run a ray tracer, you are going to get a completely converged image without any noise, without any problems. That image you can consider done. But this will not be solved with completely illumination. This is a speciality of ray tracers. But if you have such an effect, then you may have to wait until more and more of these samples are computed and the more smooth image you move. But we will talk about this effect extensively. It's going to be very important. And just an important question, what kind of material model can this be? Obviously, this is some quick perhaps open gm preview, but it's very apparent what I see in here. What kind of shading is this? Is it spectacular? No. These are definitely not here. What else? Yes, exactly. So this is the Lumberian model. You can also see this effect that it goes completely black in this facing angles.