Our next topic is Furniture Design. So the work we introduce here is a guided exploration of physically valid shapes for furniture design. So the motivation, the question we want to address here is. How to design a valid furniture like a shelf or a table. So the problem we consider is robustness and stability. Robustness means, means do not break. This one example, if you have this kind of shelf and you put a heavy object here, and this nail can be break, bent. So this is a problem we have to avoid and also if you get this shape and you put this heavy weight here, then this would probably topple. So these are the problem we want to avoid. However, in this simple case it's easy to see but if you have a very complicated shape like this one, it's very hard to see how to design valid furniture. So that's a problem we want to address and our approach is like previous systems we introduced so far, we provide continuous structure simulation. So given our user input, system applies physical analysis and you can identify whether it is valid or invalid so you can continuously provide feedback. In addition to it in this work we also provide active guidance to maintain validity. So in addition just telling you, you are invalid or you are valid. System also guides the user to recover validity. For example, if the user in this invalid region, your design is invalid and not only telling that you are bad. It can also tell you how to fix it. So the system is continuously provide active feedback how to go back to the valid region. So this is can be further assist the user in the design process, so that's the idea. And this is a specific technique we will introduce, is one is annotation indicating valid range. So here, in this angle, is not very good, so not durable. So, if you put weight here, then this nail will be broken. However, if you rotate this, plank to horizon- ah, vertical, then it becomes stable, robust, it doesn't break. But if you go beyond farther then again it's not stable, robust, durable. So system compute valid range of the angle you are manipulating and and visualize it as an annotation so internally system runs many simulations and then finds the valid regions. So this is durability analysis and annotation. So the another is stability. So here the system identifies that this configuration is not stable. If you physically fabricate this, this will topple. So this is a feedback but in addition to providing this feedback, system also provides suggestions showing valid designs. So when the user provide this, not only telling the user that this is not stable, the system generates valid candidates in this way and the user just picks one of them and then you get the valid design. So let me show you a video. [SOUND]. So, this is a user interface, so user designs the shape, with a simple dragging operations. Yeah. Nothing special so far. So here, as a user start rotating this plank. If the angle is too much, then this joint will collapse. The system provides not durable feedback. In addition, this not durable indicator, the system shows a valid range. So in this range it's okay. Yeah, so this is a visualization. So, this is much more helpful than just telling you are not durable. You can, the system also provides visual feedback. Yeah, this is a valid range for preventing toppling Our system also provides varied number of suggestions. If this is, this is geometric analysis but if it's not disconnected then system suggest multiple choices to fix discontinuity And here in this situation it will topple, so system suggest multiple candidates to fix it. Yeah, so in this case it's not durable so systems suggest to lower it, or move the lower bar or add a support. An let me show you a little bit more complicated example. Yeah, so as the design gets more and more Complicated, it's very hard to see where is the bottle neck and what is valid. But this kind of system very helpful to design physically valid complicated shape like this one. And then we also fabricated real one so in this case we designed a chair [NOISE] Okay, so let me again very briefly describe what's going on inside. So what we present is how to prevent breaking and how to prevent toppling. So first one is robustness analysis. So it analyze bend force of joints. And also in the prevent toppling we put- analyze force, contact force at the ground. So let me explain one by one. So okay let us how to, let me just describe how to prevent breaking. So, suppose we have this kind of configuration, three planks and then two nails. And then we try to find the region where the nail break. And then in- to do this we consider space spanned by nail joint bending forces. So we compute bending force at this nail 1 and nail 2, and then we put designs, in the space spanned by these forces, applied bending force applied to these shapes. For example, in this configuration, it is located here. You know there's no, if there's no bending force, lambda 2 equal zero and lambda 1 is somewhere here. So this is a basic thing, so compute bending force and then you put current design in this space and after that we have a valid range. Right? If the bending force is too light, too large, it's not durable. So bending force should be smaller than some specific threshold. And it is end up with a kind of box region. So if the design is inside of this region it's durable, it's safe, it's okay. But if it's outside it's not durable it's not okay. So system needs to suggest going back to this region. So yeah, so valid design is somewhere here. So the task is moving from here to there. So that's the starting point and then what we do is something like this. So for our given current, non-sta-, non-durable design we gradually change a parameter and then we check the trajectory. You know, gradually change the design and then you proto it in this fourth space. And then, you see a trajectory. So if you change one thing, you get this trajectory, if you change another thing, you will get another trajectory. So in the system, we test various trajectories, you know? One point we try to change the angle here, in somewhere else, you try to position something else. We tried many different variety or operations and check trajectory. And then, after checking trajectory, we pick the one just going in the safe region and then show it, as a result. So internally, systems learns a lot of physical simulation and we do not explain detail here, but internally we again use sensitivity analysis. So it is a linear approximation. So instead of computing individual one, we are approximated with a linear single line then you can analytically compute collision, safety region faster and so that's what's going on internally. And prevent toppling. So this is also very similar. So here we compute contact force between the furniture leg and also the ground. And this force should be in one direction, you know, force should be. A reaction force comes from floor to the furniture. If the force is on the opposite side, then it means that it leaves force floor and it means that there is a toppling. So in the force space diagram looks like this, so if. So contact force should be always positive. You know? Contact force needs, needs to be positive, if negative, it means that the contact becomes fall apart; which means the furniture topples or, stumbles. So, the task is to move the design back into this valid region. So again, the same thing. You compute the trajectory by checking many variations and then tries to find the good one. Ok, so a little bit, maybe too fast but that's a brief summary. So, we presented a furniture design with durability, and stability analysis. So system continuously checks whether current design stable or durable. And in addition to that, system actively guide the user to go back to the valid region. To do so, internally, we apply joint force analysis in the force space. So in the case of durability we compute bending force and for the stability we compute the contact force and then we try to move back into the safe region. So to learn more, original paper was published as Guided Exploration of Physically Valid Shapes for Furniture Design. And the physically valid design of objects is popular for topic recently, and a couple of interesting works appearing recently. And one is Make it stand: Balancing shapes for 3D fabrication. So this technique takes single 3D object and then tries to adjust the shapes so that it actually stands, not topple. So this is automatic optimization and then another is, Stress relief: Improving structural strength of 3D printable objects. So this one takes 3D object and print it. However it also analyzes the weakest bottle neck for example, this neck can easily break, so system identifies it, and then make it more stronger. So this kind of optimization is heavily explored. Our work is different because we try to guide the user during the modeling phase. Well, that's it, thank you.