Our next topic is Garment design. The work we introduce here is sensitive couture for interactive garment editing and modeling. So, the problem we want to address here, is a design of a new novel original garment. And again, this is very difficult for inexperienced people. So, you have 2D cross pattern, and then you have three dimensional garment on the body. it's, what you want is three dimensional shape. But what you have to control is two dimensional shape. And it's very difficult to imagine what 2D pattern you have to get to get the desired 3D shape. So, that's a problem we what to address. And our approach is the same as the previous one. So we learn continuous concurrent simulation behind the scene. So user continuously edits are saved 2D pattern with mass operation and the system continuously applies physical draping across simulation. So user can directly edit to decide while watching the clothing in the 3D configuration. Well, that's the idea. So the same as before, on the left side, you see 2D clothes patterns the user is editing. And on the ride si, on the right side you see clothing, putting onto the 3D body. And here the simulation is much more accurate than the one I showed for the stuffed animal design. So you can actually predict details, wrinkles and so on. So you can interactively edit the 2D pattern. And the system interactively updates clothing draping simulation results. So you can actually see some more wrinkles here. And then you can edit the shape. So as to reduce wrinkles if necessary. So traditionally, if you want to do this, you have to actually physically cut paper or a cloth material, stitch together and put on the mannequin, physical mannequin. And learn draping and see the result and then go back to the pattern and cut it again. It can be very, very long, long time, it's very slow. And those are computer based simulations also available. It's similar. You have to move the simulation engine simulation and then go back to the design. That's a problem. And also, technically, it's very, challenge to run physical simulations so rapidly. Of course there are real time rapid cloth simulation existing already. But they, these physical simulation is for animation. So they assume fixed clothes pattern. So clothes geometry doesn't change. And the system learns lots of precomputation for efficient computation real-time. And then just draping learn animation. To learn simulation to create animation. However, here, the system, the user continuously change the rest of shape. Which is, violates assumption of standard animation, animation simulation [INAUDIBLE] so that's a challenge we have to address. So if you do not like a wrinkle here, then you can just interactively add dart here. And then, you can immediately see how the resulting clothing looks more natural. Okay, so this is one example and here's more examples. So, yeah, so design of t-shirt or garment for human character is not actually so difficult. There are many standard ways to design a garment. However, if you want to design a pajama for armadillo like here, it's a different program. No one knows how to design a character shirt. And especially if you wanted to buy a physically bodied garment, it's very difficult, and this kind of design tool can be very, very useful. So previously in computer graphics, garment of this character is a very cross mesh, there's no physics, just a polynomial mesh. But recently, game engines are very fast, more efficient. So we use, people starting to use physical assimilation for these garments. Now then, it's necessary to design physical bodied garments. So that's these are why you need this kind of tools. So here is a comparison with a real one. The left side is a computer graphics view in your simulation, and the right hand side is the physical construction which we 3D printed. This kind of character and also we physically stitched together this garment. And as you see, of course, it is not 100 millimeter size exact match. However, you see the general pattern like sleeve folds here and then you see full sleeve folds here. So I think this is enough for our initial design. And we also design real size garments using system. So this is just, just screen snapshot. We're using track to edit to save. And then you see continuously see the 3D result. And then we print it into a larger format, real size print. And then you put pattern into a cross and you stitch it together and then you get a wearable results. Okay. So let me briefly describe algorithm. So, again, so oh, complete implementation is beyond the scope of this short video. But I can briefly describe the basic idea behind it. How to make it faster. So this is a fundamental equation. Mathematical representation of the problem we trying solve here. So we have 2D input pattern. This is the input from the user. So user specify 2D clothes pattern. And then what we, ha want to compute is 3D cloth shape. So, yeah. So input these XY coordinate positions or we input clothes, and the output is XYZ position or or when you give your body shape. So 3D cloth shape, this is output you want to get. And then we cover function, that represents an additional set of 2D cloth pattern input and 3D cloth shape output. And this function returns 0, if it is satisfy the physicality, body natural shape. And this function is called the resi, residual. So if the 3D cloth shape is not in the desired, appropriate physically balanced shape. This zero becomes bigger, larger. And then we, we gradually, this residual are smaller. They get more physically realistic results. So that's the problem we try to solve. And visually, the situation looks like this. So you have a space of varied designs. And on this view, on this axis, you have many different two dimensional cloth patterns. So use the space for that starts from this pattern and then moves to another pattern, and use the edit. And for each shape, you have a single iso surface, or space-specific region, where R becomes 0. So here, it's represented as a single line, single cloth line. So, for the given 2D clothes pattern, we take a look at the region where the R equals 0. And then look at the 3D shape, and then you will get the proper 3D output. So this is a, very very simplified view of what's going on internally. The program is at, notice here. So R, the residual is very highly non-linear and very, very slow to compute. So, yes, so R 0 is very curved and very complicated. When you change the pattern, you have to recompute R, which takes too much time. So we, what we use is a kind of a stanadard. But we use a linear appro, approximation around the current state. So visually, it looks like this. So, this a current design and then you compute the linear appro, approximation of this residual function. And this method called, called sensitivity analysis in structural analysis. And then after computing linear approximation it's kind of easy, to predict the, compute from 2D input to 3D shape. Just by solving our linear system. Which is faster. Of course, this is an approximation near this design. So, if you go farther away, then it's, it becomes too different. So and your system. So single linear appropriate is nothing now. Users who're walking far away from the linear state. It's a difference from the real physically realistic result gets bigger. So in that case, we compute another approximation here right this way. And then, so we cache multiple linear approximations occasionally and then blend them. So, in this case, if you have two examples and if you blend these two, you get a very, very close approximation. And this is still very fast to compute. So that's what we do in internally. So caching happens occasionally. So, the user, the system continuously monitors. Users the dragging operation. And then when the users dragging getting far away, you create another cache. Now you have two cache, and you move far away from these two caches, the system will generate another. So in this way, the system incrementally, the more and more caches. So this is a summary. So we presented garment design with concurrent physical simulation. So we edit a 2D pattern. And the system presents 3D draping results. And then we have uprising sensite, sensiivity analysis which is linear approximation. And those are multiple caches before providing rapid feedback without random simulation each time. So, to learn more the original paper was published on Sensitive Couture for Interactive Garment Editing and Modeling. And the garment design is also a hot, popular topic in graphics community. And one example is Virtual Garments, A Fully Geometric Approach for Clothing Design. So, in this project, they did not use any physical simulation. Purely geometry approach, but the, but they can rapidly generate reasonable shapes this way. Thank you.