The last topic of this week is a glider design. So the work we here, we introduce here is a pteromys, an interactive design and optimization of free form, free flight model airplanes. As you see, this is our very latest work. So motivation the question we here is how to design a paper airplane or glider so you could fly the airplane, and then we hope it flies well. However, it is not very easy for inexperienced people to design a glider that flies well. You know, there are many designs, but this is a result of many, many experimentation. It's not easy to design arbitrary shaped airplane. So that's a problem we want to address. And again, we ran concurrent simulation, but not only ran simulation to analyze it whether it runs well, we also provide automatic optimization. So given current designs system will automatically adjusts the shape so that it flies well. So, this is similar to the previous system. Behind the scene is more interesting. Here, we use a data driven approach for the simulation. So accurate analytic simulation of airflow is very difficult. So here, we use many, many measured data. So this is airplanes, we actually fabricated, created, And flew together and measured. And we get this lots of data and we infer many parameters. And then we use it for the physical analysis. So that's the story. So let me show you a video. Yeah, so this is a typical example of not flying airplane. So if you design arbitrary wing shape, you know, it just drops, doesn't fly. So our goal is to be able to design arbitrary shape, this kind of strange shape airplane by yourself that flies. And then this is one example we created and it flies really well. So, our approach is like this. So first is offline computation. So we took many, many airplane trajectories and then analyze it. So we flew these gliders, and then checked the trajectory, flight trajectory. And then we compared the simulation result, and then adjust the parameters so that simulation result fits well with actual flight. And this is the basis of the physical analysis. And given this data, now you generate, you design your own airplane, and then system now can predict the flight trajectory. And, in addition to showing and predicting the flight trajectory the said system runs automatic optimization to make it flyable. So the user can pause for edit, edit and simulation engine and then you get the desired shape. So this is our user interface. So similarly, to the previous system user edits the shape this kind of two dimensional view. So you're moving along the vertices, and then system continuously change the 3D shape. In addition to that, here, the bottom half is the simulation result. So this predicts what happens. In this case, the airplane goes upwards, and then probably goes down. And as user edits a shape, system continuously runs physical simulation, and tells whether the airplane flies well or not. The reason, why we have multiple trajectories is that, you know, the user's hand throw always changes. Sometimes goes higher. Sometimes goes lower. So the system automatically predict, consider multiple possibilities, and then shows general tendencies. So that's a feedback. And now let me describe the optimization part. So as you see, there is a magic make it fly button. So this is when you press this button, system applies automatic optimization, and make this airplane fly. So here, in this design, it doesn't fly well, it doesn't pass this line. It goes too up or too down or it doesn't fly well. As soon as you press this button, system optimize it, see it carefully, it's kind of very subtle. But I do not, nothing. The video, shows the system automatically adjust the wing position. So, let's see. The user press this button, system adjust the wing position. Yeah, you see this. So, the front wing moved sideways, so this is not by the user, the system automatically adjusts the shape so that it flies well. So in this clip, the user edits the front wing and then system automatically adjusts the position and orientation of the rear wing. So as you see, user, moves around the front wing and then system automatically adjust, the rear wing. And please note that simulation results di- drastically changes with a small change in the orientation of the position. Which is very difficult to do for the user, or people to do it, but the system can do it. [SOUND] So again the important part is this kind of interactive exploration. You can test many different things and then system continuously provide feedback. After having the design, you send the data to the laser cutter, and then you get the shape. And results. So, here's our results. So important thing is that it really flies well. You know, it's kind of amazing for us too. So this here is a launcher and then starting from it, it flies in this direction As you see, yeah, it flies way back, so it's very amazing. Yeah, we have it here. This dragon airplane, and this also flies. You can also use other materials. And this one. Or this one. Okay. That's the video. So, here's a summary of the algorithm that we use. So, standard fluid simulation aerodynamics is too slow. It's not, can be a real time. So we use a traditional wing theory. Wing theory is simplified model of our airplane. So it computes lift force occurring each wing, and then after computing the lift force and gravity and others, and then you can predict the flight trajectory. So that's the theory we use. So wing theory looks like this. So given a, given a wing, shape, and then the force. We compute, force up, coast by the wing. So this is the lift force, f, and then drag force, fd, and then rotation force in tau- tau. And then it's a function of velocity and area, you know. It's faster and faster and then forces gets bigger, and the area is bigger, and then forces gets bigger. And the question is these parameters. You know, these are the constant. Defines the behavior of the wing. And it depends on the angle of attack and also depends on the shape of the wing. And these parameters are what we want to know. So to estimate this parameter, we take our data driven parameterization approach. So we fly many airplanes and then measure the parameters and then we try to fit the parameters. So, you know, this Cd, Cl, Cm, are all depending on the angle of attack. And then we plot it in a measured- we plot the measured data in the space and then we get a best approximation. And also we then, we can estimate the force caused by each wing element in this way. And then we aggregate forces caused by these small wing elements. And then we compute the approximate, total force caused by the total entire wing. So to learn more the original paper is published as Interactive Design and Optimization of Free-Formed Free-Flight Model Airplanes in 2014. And flight simulation is also discussed in graphics community. One example is data-driven control of flapping flight. So it simulates the flapping flight of birds. And data-driven simulation is also a popular topic. So you, it is- it’s often the case too slow to simu- run standard simulation. So possible approach is to run many, many simulations beforehand offline. And then in a runtime just assemble, measured previous simulation result to get the realistic result. And one possible reading is Data-driven simulation methods in computer graphics published as a SIGGRAPH 12 course material. So this is a summary of this week. So we presented integration of real time physics into modeling. So user continuously edits the shape, and then system continuously provides feedback, running physical simulation. And some systems just provides ’yes or no’ simulation results. But, also some system provides continuous guidance to design valid shapes. So we introduce a first, simple cantilever design, and also design- discuss musical instruments with Eigenmode analysis. And also garment design, using linear approximation and furniture design with active guidance using joint force analysis, and finally glider design using wing theory with data-driven parameter fitting. So, that's the end of this week. Thank you.
