 Thank you, everyone, for coming. Thank you so much for the organizers for letting me give this talk. It has been a dream of mine to attend the Blender conference since Blender 2.5, so quite a while. And well, I'm Matias Garate Silva. And today, I'm going to tell you all about how to model impossible figures. I'm going to start by giving you the spoiler of what is the secret behind modeling these possible figures before I tell you everything about how to model the impossible figures. But before I get into that, I want to tell you a little bit about myself and how did I got here. So my background is actually in astronomy. I like mathematics, programming, physics. And I use that to study how the solar system forms through numerical simulations. And occasionally, also do some visualizations in Blender about that. And on the other side, I also love digital art, Blender in particular, of course. And especially geometric art, surreal art, low-poly art, everything that is very geometry and kind of cute. All of that I like. But I mostly kept those things separate, like always going in one thing on the side, one thing on the other side, and not really mixing completely the two together. But that changed a lot when I played this game, which is called Monument Valley by Os two Games. It came out 2014, in which it's a puzzle game in which you explore these impossible architectures with your character and solve puzzles using impossible figures. And they have a second release in which they really bring dozens of new levels and scenarios with these impossible geometries that create this optical illusion that you are not sure what is up, what is down, what is floor, what is behind, and what is in front. And all these tricks that it plays with the mind, the aesthetic that it uses, this very nice aesthetic, really struck a chord on me on the artistic side. And also on the mathematical programming side, because of all the, what is the principle behind this? How do you, how does this work? How can I do this? So I decided to learn how to do it myself, and that is what I want to share with you today. So how do we make impossible figures in 3D? So I already gave you a little bit the spoiler, but now we are going to go through it step by step. So the first ingredient is the isometric camera, and in particular the true isometric camera. So not just setting the camera to orthographic, but also to put the camera rotation in the X coordinate at 64.736 degrees. We will see later why that number is important, and 45 degrees around the C axis. And that gives you the true isometric camera, which has the very special property that when you look at a cube, for example, you will notice that the Y, X, and C edges are all the same size in the camera view, in the projected view from the camera. That is, if you trace a circle around it, they will all be centered at the circle and have the same length. Now, why, how can we use this to make impossible figures? With that property, you can actually buy, build a skeleton for your impossible figure. You can move in the Y axis, then in the X axis, and then in the C axis, and go back to the origin from the camera view. So in this example, I move five units Y, minus five units X, minus five units C, and I went back to the starting point. But in the 3D viewport, we see that the starting and the end point are actually very far from each other. So we are playing with the perception of depth of the viewer. Now, using this skeleton, we can start by blocking out our figure. We can put a block in each of the corners. Then we can try to connect these blocks with edges. And we will notice that when we try to do that, the viewer can see that one block, the yellow block, the last one is behind the pink block. So the viewer can notice that the figure is disconnected. Let's try that again, but with another block in the front. Now the viewer can still see the disconnection, but on the top of the figure. So how do we convince the viewer that this figure is actually connected? Well, we use a tool that is not advertising of, the bisect tool. It's on the same location of the knife tool. And what it does is it creates a cut across a line. And if you make this cut from the camera perspective, from the camera view, then this cut will be perfectly aligned with the camera orientation. Then you can rip the selected edges and delete the parts that you don't need, go into the disable the overlays, and you have your first impossible figure. And this is really the starting point. Thank you. Before I continue, can someone please take a picture and send it to me? I need to remember this. I'm super excited. Thank you all. OK, that is who you make your first impossible figure. And then using this principle, you can actually build more complex impossible figures using the same principle, and continue going. And continue going. In this case, we're moving the y-axis, c-axis, compensating the x-axis, and back to the starting point. And with that principle, you can start building more and more impossible figures. You can notice that sometimes you can skip the last point of dissecting if your figure allows it, but that is case-to-case basis. You can continue adding edges to make this illusion more complex, but I found out that the more edges that you add, then there is more troublesome for the viewer to perceive the illusion. So I usually stop at five. These are a lot of steps, but you can also skip them if you download the Paradox Toolkit add-on from GitHub that I released a few years ago. And this is basically a library of impossible figures that lets you create these five base meshes. OK, I'm sorry. I was looking at different screens, at different time skills. OK. And the Paradox Toolkit is basically a library of base meshes of impossible figures. So with these base meshes, you can start your impossible scene and add more things on top. The way to use the add-on is very easy. You install the add-on, you create your orthographic camera, you add your first impossible figure, and you can even play with the dimensions of the figure, the length, the thickness. And with this add-on, you can actually break the first rule that I mentioned of impossible geometry. That is, you can skip the isometric camera and use any orthographic camera. And the add-on will calculate what is the length that the figure needs to have in order to go back to the starting point. So you can go for more creative impossibilities. Or you can use these figures as building blocks for even more complex figures. So in this case, I use the different variations of the triangle and the rectangle and match them together to create very complex impossible geometries with several disconnection points, so to call it. So there are several points in which you convince the viewer that the figure is connected and in reality is disconnected. So there's no rule that says that you have to only include one figure. You can include multiple. OK, so far. So far, I have told you that you need an orthographic camera that you need to, preferably an isometric camera, but you can skip that if you use the add-on that calculates all the math behind it. If you want to know all the math behind it, then you can also talk to me in the coffee break, because I love to talk about that. But I still haven't told you how to render impossible figures, because after you finish modeling, of course, there comes a whole new beast that is lighting, materials, rendering, and so on. And I'm going to use this scene as an example of how do we do this. I'm going to break down this scene a little bit. So in the screen, you can see a building. And I'm pretty sure that you are already starting to notice something weird in this building, right? We have three floors, but the middle floor appears to be taller on the left than in the right. I'm going to reveal now where the illusion is located. So this figure is, of course, disconnected at some point near the base. And now let's see how we light and render this figure. No. First thing, use EV, because you need a restoration engine in order so that you don't have the information about depth. If you use cycles, you will usually get some type of depth information in the number of rays that arrive from one place from the other, et cetera. It will somehow tell you where the illusion point is, and you want to prevent that. Now, the next thing that you might want to do is to add the global lighting. So for that, you might want to use a sun lamp, perhaps. And you will immediately notice a problem. If you put a sun lamp, it is very likely that your figure is going to cast a shadow onto itself. So here you can see the front part casting a shadow on the back. And this is telling the viewer, OK, this figure is actually disconnected because one part is casting a shadow on the other. So the way to walk around that is to disable the shadows. So disable the shadows from your sun lamps, always. Or just don't use a sun lamp and use an HDRI lighting from HDRI heaven, and that also works. And then you get your global lighting without telling the viewer where the illusion point is. Now, then after the global lighting, of course, we want the localized. We want the key light, the field light, the rim lights, et cetera. And here I added one first field light on the base of the building, and everything is OK so far. But if I have a second light here, you will notice that the intersection where the illusion is, one side is more illuminated than the other because the lamp is closer to the far side of the building. So how do we get a turn around that? Well, this is where it starts to get tricky, but it's possible. You have to add a second light that is a link duplicate of the first one. So you want to make a link duplicate of the light so that they always have the same information, the same power, the same color, the same size, et cetera. All the same. You have to link them together. I use the child off to handle the translation and the copy rotation and copy scale to copy the rotation and scale of the original light into the secondary illusion light. And you have to place them together so that they are at the same relative distance from the illusion point. So you can put them together at a common reference point and then move them together. And if one is parented to the other by a child off, then they will move together. And an additional bonus, you might want to also, for most of your local lights, you might want to use the custom distance so that you prevent the light that is further up to illuminate a second time the region that is already illuminated by the first light. Also to prevent a light, for example, from illuminating your illusion point, that part you want them to have uniform illumination. All about impossible geometry is convincing the viewer that you have a continuous figure, a continuous figure in the geometry, a continuous figure in the normals, a continuous figure in the lighting, in the edges, et cetera. So that is actually the part that is most complicated of this, even more than the modeling. So to make a lighting that you like and that doesn't break up the illusion and finally, one final thing that you can do, and this is the one that is most case-dependent. So this is very specific for each scene. This is the only scene in which I actually have achieved doing it, switching from an orthographic camera to a perspective camera. So here we have an orthographic camera. So in orthographic cameras, all the you don't have for shortening, you don't have depth. And that can be sometimes a little limiting. So everyone that has done low-poly modeling knows that in isometric renders know that you miss something when you lose the perception of depth. But if you model your figure in orthographic camera and then switch to perspective camera, then you might find that you can only need to make very little adjustments in the orientation to keep your illusion intact. So in particular, prefer long focal lengths because longer focal lengths are more similar to an orthographic camera. So this is 75 millimeters. It's higher than the default of 54. And you may also want to do some fine tuning. In this case, you can barely see it, but the front part of the building is overlapping the far from the back. So with a small shape key, I just add the correction to complete the illusion again so that the viewer has really no clue where the disconnection is. And using these techniques, then you can start making scenes with more complex lighting. So you can start getting creative. So in this two scene, the one on the left is disconnected at the bottom corner. And my main struggle was to include, make the illumination consistent. There are like four lamps hidden in there to make the illumination uniform. And the shadows. The shadows also need to be consistent. So in this case, I added, through post-processing, I rendered the shadow that the hinges cast on the wood twice in order to include them in the final image. And on the scene on the left, the cut is actually, the illumination of the cut comes from local lights and from emission light and from emission shaders. And the shadows of the cut are alpha planes, are transparent planes with a black gradient in order to make it look like it has presence on the ground. To make it look like the cut is really, city is really standing on the ground. So what comes afterwards, you make your scene and what comes afterwards with this very niche skill. Well, you could try to use it for a level design. So you can make really creative puzzles with this as Monument Valley 1 and 2 from most two games showed. The game is amazing. Like, I really cannot recommend you enough to play it. You could also make an illustration that is very eye-catching. So these impossible figures have the property that they really catch your attention because your brain is really struggling to figure out what is going on here. So they are very good for grabbing the viewer's attention. But for me, in particular, what comes after is printing them. I like to print my work in physical, in a final paper. And last year, I had my first solo exhibition with my work in the city of Heidelberg in Germany, where I exhibited for the month of October my collection of paradoxes. And it was really a rewarding experience to have the people come be fascinated, intrigued, and talk to them, and just interacting with the work. In the exhibition, I also include early sketches. I included some images that are the ones that I showed here, the reveals of how the solution work. And afterwards, one artist that saw my work in this exhibition also invited me to participate in a collective exhibition in Herzheim earlier this year in the Kunstgarten by the Collective Station creation. And then I met a lot of other artists that were super. It was just a very, as you all know from this company, it's a very enriching experience decision. He was the one that invited me to participate. So everyone really nice and really a wonderful experience. So now the final step, no, not the final. The next step for me is to open an online shop for my prints. I really want to sell my work online and to just let people enjoy it in the physical form. And I'm preparing a new collection of impossible geometries for this. This is the project at its early stages when I only have the sketches. This will come to Blender and then will be printed in high quality. You can find more information on my Instagram or just come talk to me afterwards. I actually have some of my prints with me if you want to see them in physical or if you want to take one home with you. So thank you so much for listening.