 Okay, so I don't think I started. I will show you some of the small paint contest assignments from previous years. Is this visible? Is this? Looking to the one, I think I should pull some of the curtains. Maybe I'll be honest with you. Just a thanks. How about that? So you can see that even with the small paint program, you can make incredible, incredible scenes. So this is the thanks. So this is the state of the art lecture. Basically what we are interested in, this and the next lecture, is starting from the very first algorithm that was ever created to solve the rendering equation, a classical path eraser, up to the most sophisticated works, some of them, which came out less than a week ago. And I won't go into deep mathematical details for most of these techniques. What I would like you to know is the basic idea and intuition behind the method and why we are doing the things we do. So deep mathematical details will also be there in the form of links where you can look behind the curtain and you will see what is exactly going on in there. Now before we start with the state of the art part, there's a few things that we need to discuss. One, this person. So we have talked about indices of refraction. The index of refraction for different materials, what was it? It was a number. So in every code, in every program, in every theory, we use numbers. Well, in reality, indices of refractions are not numbers. They are, in fact, functions. What does it mean? They could be functions that depend on the wavelength of incoming light. And what it exactly means is that there are materials that refract incoming light of different colors took different directions. And that's quite profound because you will see the beautiful effects of dispersion in a second. And there are also some supplementary videos that you should take a look at. This is a good example of it. This is a prism. So you can see that the incoming light is white and the prism does break down to this white incoming light to all possible colors there are. Another good example of this is rainbows. So whenever you are on a family trip and they are asking what you're looking at, and if you accidentally don't say rainbows, you will maybe say dispersion. And they will put you in an asylum instead. But don't worry. You are correct, scientifically, and that's all that matters. You can also see, and maybe not so beneficial and not so beautiful effect of dispersion. It is called chromatic aberration. This means that we have a camera lens that is possibly not the highest quality, and it can introduce artifacts like this because different colors of light are reflected into different directions. And you don't get the sharp image that you would be looking for. Now this is dispersion rendered inside LuxRender. So you can see that with physically based rendering, you can actually capture this effect. And you can also render diamonds. So if you have a fiance and you would like to buy a ring, but you are broke because you're a university student, then you can just render one. And you can also render one with dispersion. But see if you have a nerd girlfriend because if so, then maybe she will be happy about it. And most people aren't. And I speak from experience. And you can also see this really beautiful effect in the old, old pink-cold album cover called The Dark Side of the Moon. There are also some videos about this in the internet rendered with LuxRender. Take a look. Now, the first question is, is the index of refraction of glass constant? Well, let's look it up. Obviously we may have glasses that are made and manufactured in different ways. There are most of them are not completely clear. They are some kinds of a mixture. So there are different kinds of glass. But let's just pick one randomly from a database that gives you indices of refraction. And you can see that it is actually not flat. It is not a constant. There's something happening in the function. So this means that there are glass types that have dispersion effects. And even only slightly because you can see that between the minimum and the maximum there is not such a large difference, but there is something. So you could say that at least this kind of glass introduces some degree of dispersion. So let's take a look. What do you think about this image? Does this caustic have any kind of dispersion effect or does it not? What do you think? Is it a bit more colorful around the edges or is it completely white? Looks exactly. Looks exactly. Looks a bit red. Could be. Give me one more opinion. What do you think? It's a little bit rough. It's a little bit more. It looks like a rainbow or something. It might be a rainbow, but it may be significantly smaller. So maybe you would have to zoom in really close to Cedar Rainbow. So this is up for debate. We could see that the IOR seems to be non-constant. And therefore there should be a dispersion effect. Some artists claim that they can spot a difference between a physically based renderer, even for materials like that, and simple RGB rendering, where you cannot render these dispersion effects correctly. This is up for debate, whether you can see it, but science says that yes, there is, even if there is a slight difference, there is a difference. If you'd like to know more about this person, there is this wonderful series called Cosmos, a space time on the C. Have any of you heard of this before? Raise your hand. Okay. Few of you. So this is hosted by the magnificent Nile de Grasse Tyson. Yeah. Nile de Grasse Tyson. And you should absolutely watch it. So everyone who hasn't watched it yet, I'd like to hear your excuse, or at least I'd like to hear that you will go home and watch it. So this episode is about that dispersion mostly, and you will know all about dispersion if you watch it. Okay. Now we have another question, because we have written an RGB renderer. So we, if you look at the source code of small paint, everywhere you just see RGB, RGB, RGB. How do we write a correct physically based renderer? And even before that, how do we even represent light in the visible spectrum? Now a good answer to this is to introduce a function that describes how much light is carried at different wavelengths. Now this would be a continuous function that we could call spectral power distribution. And you can see that at these lower wavelengths, there is not too much light carried on the higher wavelengths, there is more. So you can put this representation into your renderer. And what you would do is that you would just a naive solution, you would pick a randomly chosen wavelength. And you would trace it into the scene using this wavelength. And if you do this, you can actually do another kind of Monte Carlo integration, because you would also add one more dimension of integration, and this one more dimension would be over wavelengths. Because you would also be statistically taking random samples of the rendering equation for a given wavelength in a given color. And then you would need to sum it up somehow to get a sensible solution. There is more about this in PBRT, Chapter 5.