Okay. So, next topic is, the design of novel musical instruments, like a metallophone. The title, we introduce, the work of the, work, the work we introduce here is titled Designing Custom-made Metallophone with Concurrent Eigenanalysis. So the problem we want to discuss in here is to, how to design an original musical instrument. So, we pick metallophone, in this project. And as you see, it is very difficult to find a proper shape that produce appropriate sound. You know, in order to function, as a musical instrument, they need to produce appropriate sound. However, it's very difficult to predict what sound they produce when they're hit by a stick. You know? So that's a very, again, very difficult constrained design problem. However, if you have a computer, computer can predict the sound. And if you run it, continuously, and rapidly, it can be very useful. So user edits the shape, of a bar, of a Metallophone and the system continuously learns physical simulation to predict the feedback or audio they produce, the tone. And then user see, hear the sound. And then, if it's too high, then it goes back to the previous one, or it's too low, go to the other side. So in this way, the user can interactively explore, a valid shape, while also searching for aesthetically pleasing shape. So that's the idea. Let me show you a video. Okay, so here is a video. In this example, the to- [BLEEP]. >> So here, on the right side, you see a two-dimentional pattern, of a Metallophone you are designing. So this is a standard, editing software. You can change the shape by dragging. And on the right side you see that the simulation result. This visualize what happens if you hit this metal bar, with your stick. No no, If you stick the bar, it vibrates and then produce sound, and this is a visualization of the vibration. Of course, this is exaggerated, but you see the result. And then, in addition to it system also produce the sound, predicting its tone, or pitch. So user can hear it, using your ears. So while hearing your sound, you edit the shape. And so that you get interesting shape. But also satisfies the desired sound. >> tone of a Metallophone is calculated via Eigenvalue analysis [BLEEP]. As the user edits the Metallophone shape in the left window, the system immediately computes it's Eigenmode. Shown in the right window, which tells how the Metallophone oscillates in 3D space. Its tone is also updated with oral feedback using beep sounds, and visual feedback in the status bar. [BLEEP]. Because the change of tone caused by the shape edit is very difficult to predict, we believe designing a Metallophone with the desired shape and tone will be possible only with a responsive FEM. >> So, by the way, this visualization is actually also useful when you, physically assemble the Metallophone. You know Metallophone in order to, in order to make a Metallophone you have to put this bar, onto the base. However, its question is where to fix. In this view, you can see that this part is vibrate a lot. So this part should not be fixed. But this part and this part is not moving at all, so this is a good place to place it down. [BLEEP]. >> Here are, the designed Metallophone pieces by an artist. [SOUND]. And its actual creation. [SOUND]. This shows that our analysis successfully simulates the real world. [SOUND]. Yeah. So, again, I think this kind of design's very, very difficult with offline simulation or existing method. Only with continuous feedback, you can explore many possibilities very rapidly, and you can design this kind of interesting shape, with appropriate sound. So yeah, so algorithm, we, we briefly describe the algorithm. Again, we use finite elements simulation, so we do not go to the details. But I can give you an, a basic idea. So the problem is to find frequency of vibration. And here, the method we use is Eigenmode analysis. Let me give a very, very brief abstract explanation. So this a equation defining this phenomenon. So, this is basically like a very basic a spring system. So u, u, means the displacement, or location. And then, Mu, this one is acceleration or the position. Which which is proportion to the force. So this means that, As the displacement is proportional to the force, applied to the material. So this is basically the same as a spring. You know, if you spring, more, move- If you move more, than the po, force to pulling back is gets larger. So this is a very basic and governing equations, for the system. And then u, we represent u, we assume oscillation, so vibration motion. Which is presented as this one. So, left side is amplitude field. So amplitude is depending on the X. This is the view you see in the right side of the window, you know, the amplitude. So amount of vibration is dependent on the location. Some part moves a lot, some part doesn't move a lot. So this is the left side. And right side is just sine wave, in oscillating motion. And we put this into here. So amplitude is positional, and the oscillation is depends on the time, and very yeah cyclic motion. And then if you put it here, and then swap the equation and beautify it, and you'll get it. And this is very standard Eigen value problem. And you can solve using standard matrix computation method. And after solving this one, this w, is directly associated with the frequency. So after solving this Eigen value problem, you'll get the frequency. This is the sound we, we produce as a result of simulation. So here's a summary. So we presented Metallophone design with cons- concurrent simulation and audio feedback. And in, inside the system we ran standard Eigen mode analysis. We assume cyclic motion, and then we tries to, to find the frequency. So to learn more. Original paper is published as Designing Custom-made Metallophone with Concurrent Eigenanalysis. And for if you want to know more ay- analysis one possible reading is, Dynamics of Structures. This is old text book. And also sound rendering. So simulation of sound produced, production. Sound synthesis and sound propagation is also a hot topic in computer graphics field. So it's called sound rendering. And one interesting paper to read is recent one, is Precomputed Acoustic Transfer. Output-Sensitive, Accurate Sound Generation for Geometrically Complex vibration. So, these are the recommended readings, if you want to know more. Thank you.
