COMP Sound Simulation Final Project Report Generating Synthetic Sound of Thunder

Transcription

1 COMP Sound Simulation Final Project Report Generating Synthetic Sound of Thunder Sang Woo Lee 1. Introduction Thunder and lightning is most exciting and astonishing nature phenomenon. It is also a dangerous and frequent natural event. It was even a major element of nature worship for ancient people, and the symbols of numerous Gods. Understanding the thunder and lightning is very important for numerous purposes. The most important purpose is preventing damage from the lightning. Recently, for the computer graphics, it is important that to simulating the visual of the lightning and sound of the thunder. To simulate natural event in virtual world, the lightning and thunder are very important element because it is dramatic and frequent. There are various researches for simulating lightning, like [1] in Gamma lab at UNC. However, there are a few papers ([2], [3], [5]) related to simulating sound of the thunder. Therefore, this project s goal is simple: generating physically based sound of thunder. Similar to other sound simulation, it is quite changing and needs dense computation. 2. Previous works In [2] and [3], The Digital Ceraunoscope: Synthetic Thunder and Lightning, the author generated thunder sound which is based on the geometry of lightning bolt. This papers modeling of thunder sound is mainly based on [4], and their reasoning is useful for determining a shape of hidden lightning bolt. Because the thunder sound is consisted by shock wave from lightning heating, it is reasonable to consider lightning geometry to simulate thunder sound. Moreover, we can use this algorithm for designing lightning and thunder as we design. There are so many variables to be considered to simulate the sound of thunder, like atmosphere disturbance, absorption, refraction, wind shear, and [4] mainly denoted about air refraction by temperature, and air absorption. In [5], they introduced simple and fast algorithm to generate lightning geometry in real time using GPU. They associate their lightning algorithm with [3] s sound of thunder generating algorithm, which is based on WMwave. 3. Methods 3.1 Generating lightning geometry I implemented my lightning geometry mainly based on [2] s algorithm, because its lightning structure is based on [4] s research, which is most suitable for my project. However, there are some missing links in the paper [2], so I should find some hidden values and added some of my own algorithms and optimization. In [2], there are two pass algorithms: first pass is generating large scale structure, and second pass is generating small scale tortuosity from the first pass large scale structure. One first large scale structure, he used parameterized values for the length of the lightning stroke line segment with height, and used it as a probability density function. However, his function was not suitable for PDF, because it is not converge when you integrate it from infinity to infinity, and also has minus values in its range. I asked Glassner about this, but he didn t remember how he had done. Therefore, I just used my own reasoning to make it useful and reasonable. I found the graph of the parametric function in [2], and I would choose values of start and end closed to them. I found that when I cut the function from y=1 to 7, it approximated the original graph in [2]

2 close enough. It is also reasonable because the average height of lightning cloud is 6km, so using y with 6 ranges is reasonable for me. I also set and used a threshold from the maximum length, because without maximum length threshold, the randomized line segments are sometimes over 1 km and over. I used Google image searches to find 67 lightning pictures, and I found the length of large line segments are not over the 1.0km approximately. Therefore, I used 1.0km as the threshold value for the first pass large scale line segments for this. I used same method to advance the dart leader, using the average vector of previous four line segments and using the 30 degree cone to find the next advancing point with randomized selection. He also didn t explain the dart leaders splitting clearly. With his explanation, the generated lightning shape should be binary tree, which could not be the shape of lightning. Therefore, I also limited the maximum branch number of lightning tree, and it works great. I found the value 8 is most suitable and similar to the shape of real lightning shape. For small scale tortuosity, the small line segments size should have mean value of 3m. Glassner used a radius of 25% length cone to find next advance points, but with just selecting random points, it became unrealistic shape. Glassner didn t announce the values for the proximity for the next advance point clearly, so I found my own optimized one. I used 30 degree cone same method as used in the large scale shapes, and it works fine. 3.2 Generating sound of thunder It seems trivial to generate sound of thunder from the lightning shape, but there are also some of hazards. In [4], they simulated sound of thunder using WM wave. They modeling with spherical impulsive sound sources along the lightning line segments, each emits shockwave simulated by N wave. We can approximate the sum of N waves emitted by the point sound sources along lightning line segments using WM wave. In [4], they considered about two main factors: air refraction and air absorption. Air refraction could be simulated by large curvature due to the temperature differences. The increased flight time of WM wave can be simulated changing Phi and B values in the equation of WM waveform. Air absorption could be simulated by low pass filter, but it seems to be changed by the distance between lightning and observer. There are some experiment data in [6], but it does not clearly state the function of distance and air absorption. According to [6], almost no frequencies over 500Hz cannot propagate to observer. I found that thunder sound from distance lightning could be easily simulated by simple low pass filter, but it is difficult to determine how to cut off highfrequency waves from different distance. I used simple low pass filter of butter in MATLAB, but it seems to cut too many peaks in waves, so I used sound program to cut off for various frequency thresholds. The most difficulty of generating sound from lightning geometry was density of computation. It is too slow to calculate WM wave for all the small scale line segments! For 6km height lightning, the length of wave file length for 3km distance listener is about 20s, and there are 5000~10000 segments for the lightning geometry. Therefore, it should calculate about 20*44100*10000 double precious floating points! It takes over 2 hours from my desktop computer, and eats up over 1 Giga bytes of virtual memory. Intel and AMD have no choice but to love this super computational process! 4. Result 4.1 Straight lightning channel Using 3m segment Segment Number: 1660

3 <Left : Lightning structure, Right : Waveform of 0.5km distance observer> < Waveform of 3km distance observer> As expected, the straight light channel has just one big thunder clap and small rumbles. Small rumbles are due to the small scale tortuosity, which generated from pass two. As you can see, the result is quite different from 0.5km to 3km. For 0.5km observer, the big thunder clap attenuates very fast, but for 3.0km observer, there are thunder clap is attenuates slowly and lasts long. I tested no refraction in 0.5km, 1km, 3km, but there is almost a very slight difference with result using refraction. Because the refraction is removes small scale tortuosity around the ground, so there are no significant difference for perception. 4.2 Various lightning structures Using 5m segments, 6 maximum branches Segment Number: 5514 <Left : Lightning structure, Right : Waveform of 1km distance observer> < Waveform of 2km distance observer>

4 < Waveform of 3km distance observer> The waveforms are quite different from different observer, due to the difference of angles from observer to line segments. For short 4.3. Various lightning structures Using 5m segments, 8 maximum branches Segment Number: 7435 < Waveform of 0.5km distance observer from North> < Waveform of 1.0km distance observer from East> < Waveform of 2.0km distance observer from East>

5 < Waveform of 2.0km distance observer from West> < Waveform of 3.0km distance observer from East> < Waveform of 3.0km distance observer from South> As we can expected easily, not only the distance but also the orientation of observer affects the result waveform Various lightning structures Using 5m segments, 8 maximum branches Segment Number: 7515

6 < Waveform of 0.5km distance observer> < Waveform of 1.0km distance observer> < Waveform of 3.0km distance observer> 4.5. Various lightning structures Using 5m segments, 8 maximum branches Segment Number: 8472

7 < Waveform of 0.5km distance observer> 4.6. Various lightning structures Using 3m segments, 6 maximum branches Segment Number: 9530 < Waveform of 1.0km distance observer> 5. Conclusion Generating realistic thunder sound is quite difficult and need dense computation. I compared my result to real thunder sound and the result from [5]. Actually, generated sound seems to be perceptional thunder sound from distance. For close distance like 0.5km, it should include more high frequency waves, but determining the threshold for low pass filtering is difficult. It seems that real thunder seems to be more clear, and [5] s result is less clearer than real ones but clearer than my waves. That might be they use more filters than I used, which is just a low pass filtering. Otherwise, they might use more accurate and dense lightning structure than mine. I looked into waveforms, and I think that their waveform has more segments than mine. Because the number of segment determines the detailed thunder signature, it is important to make enough segments. For my result, it seems that lightning structure using more segments generate more fluent sound. However, all of my result are using more than 5000, and if the [4] s reasoning is correct, my lightning already has enough segments. Also, there are no significant perceptional difference between segments 5000 lightning and lightning. Therefore, I could not figure out clearly what the cause of the difference. Also, it is very difficult process to distinguish sound difference between similar patterns. 6. References:

8 [1] T. Kim and M. Lin, Physically Based Animation and Rendering of Lightning, Proceeding of Pacific Graphics, 2004 [2] Glassner, A., The Digital Ceraunoscope: Synthetic Thunder and Lightning, part1, IEEE computer graphics and applications, 20(2), pp , 2000 [3] Glassner, A., The Digital Ceraunoscope: Synthetic Thunder and Lightning, part2, IEEE computer graphics and applications, 20(3), pp , 2000 [4] H.S. Ribner and D. Roy, Acoustics of Thunder: A Quasilinear Model for Tortuous Lightning, J. Acoustical Society of America, Vol. 72, No. 6, Dec. 1982, pp [5] Matsuyama, K. et al., Real time Sound Generation of Spark Discharge, pg, pp , 15th Pacific Conference on Computer Graphics and Applications (PG'07), 2007 [6] H. E. Bass, The Propagation of Thunder through the Atmosphere, J. Acoust. Soc., Am 67, 1959~1966 (1980)