KleinPAT: optimal mode conflation for time-domain precomputation of acoustic transfer

Abstract

We propose a new modal sound synthesis method that rapidly estimates all acoustic transfer fields of a linear modal vibration model, and greatly reduces preprocessing costs. Instead of performing a separate frequency-domain Helmholtz radiation analysis for each mode, our method partitions vibration modes into chords using optimal mode conflation, then performs a single time-domain wave simulation for each chord. We then perform transfer deconflation on each chord's time-domain radiation field using a specialized QR solver, and thereby extract the frequency-domain transfer functions of each mode. The precomputed transfer functions are represented for fast far-field evaluation, e.g., using multipole expansions. In this paper, we propose to use a single scalar-valued Far-field Acoustic Transfer (FFAT) cube map. We describe a GPU-accelerated vector wavesolver that achieves high-throughput acoustic transfer computation at accuracy sufficient for sound synthesis. Our implementation, KleinPAT, can achieve hundred- to thousand-fold speedups compared to existing Helmholtz-based transfer solvers, thereby enabling large-scale generation of modal sound models for audio-visual applications.

References

1. T. Akenine-Möller. 2002. Fast 3D Triangle-box Overlap Testing. Journal of Graphics Tools 6, 1 (2002).
2. A. Allen and N. Raghuvanshi. 2015. Aerophones in Flatland: Interactive Wave Simulation of Wind Instruments. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2015) 34, 4 (Aug. 2015).
3. M. Bebendorf. 2000. Approximation of boundary element matrices. Numerical Mathematics 86, 4 (01 Oct 2000), 565--589.
4. Mario Bebendorf. 2008. Hierarchical Matrices - A Means to Efficiently Solve Elliptic Boundary Value Problems. In Lecture Notes in Computational Science and Engineering.
5. M. Bebendorf and R. Kriemann. 2005. Fast parallel solution of boundary integral equations and related problems. Computing and Visualization in Science 8, 3 (01 Dec 2005), 121--135.
6. S. Bilbao. 2009. Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics. John Wiley and Sons.
7. S. Bilbao. 2011. Time domain simulation and sound synthesis for the snare drum. Journal of the Acoustical Society of America 131, 1 (2011).
8. S. Bilbao. 2013. Modeling of Complex Geometries and Boundary Conditions in Finite Difference/Finite Volume Time Domain Room Acoustics Simulation. IEEE Transactions on Audio, Speech, and Language Processing 21, 7 (July 2013), 1524--1533.
9. S. Bilbao and C. J. Webb. 2013. Physical modeling of timpani drums in 3D on GPGPUs. Journal of the Audio Engineering Society 61, 10 (2013), 737--748.
10. N. Bonneel, G. Drettakis, N. Tsingos, I. Viaud-Delmon, and D. James. 2008. Fast Modal Sounds with Scalable Frequency-Domain Synthesis. ACM Transactions on Graphics 27, 3 (Aug. 2008), 24:1--24:9.
11. D. Brunner, M. Junge, P. Rapp, M. Bebendorf, and L. Gaul. 2010. Comparison of the Fast Multipole Method with Hierarchical Matrices for the Helmholtz-BEM. Computer Modeling in Engineering & Sciences 58 (03 2010).
12. J. N. Chadwick, S. S. An, and D. L. James. 2009. Harmonic Shells: A Practical Nonlinear Sound Model for Near-Rigid Thin Shells. ACM Transactions on Graphics (Aug. 2009).
13. J. N. Chadwick, C. Zheng, and D. L. James. 2012a. Faster Acceleration Noise for Multi-body Animations using Precomputed Soundbanks. ACM/Eurographics Symposium on Computer Animation (2012).
14. J. N. Chadwick, C. Zheng, and D. L. James. 2012b. Precomputed Acceleration Noise for Improved Rigid-Body Sound. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2012) 31, 4 (Aug. 2012).
15. H. Cheng, W. Y. Crutchfield, Z. Gimbutas, L. F. Greengard, J F. Ethridge, J. Huang, V. Rokhlin, N. Yarvin, and J. Zhao. 2006. A wideband fast multipole method for the Helmholtz equation in three dimensions. J. Comput. Phys. 216, 1 (2006), 300--325.
16. D. Ciscowski, R. and C. A Brebbia. 1991. Boundary Element methods in acoustics. Computational Mechanics Publications and Elsevier Applied Science, Southampton. UK.
17. P. R. Cook. 2002. Sound Production and Modeling. IEEE Computer Graphics & Applications 22, 4 (July/Aug. 2002), 23--27.
18. W. W. Gaver. 1993. Synthesizing auditory icons. In Proceedings of the INTERACT'93 and CHI'93 conference on Human factors in computing systems. ACM, 228--235.
19. Gene H. Golub and Charles F. Van Loan. 2013. Matrix Computations (4th ed.). The Johns Hopkins University Press.
20. N. A. Gumerov and R. Duraiswami. 2005. Fast Multipole Methods for the Helmholtz Equation in Three Dimensions. Elsevier Science.
21. R. W. Hamming. 1998. Digital filters. Courier Corporation.
22. Doug James, Changxi Zheng, Timothy Langlois, and Ravish Mehra. 2016. Physically Based Sound for Computer Animation and Virtual Environments. In ACM SIGGRAPH 2016 Courses. ACM, 22.
23. D. L. James, J. Barbic, and D. K. Pai. 2006. Precomputed Acoustic Transfer: Output-sensitive, accurate sound generation for geometrically complex vibration sources. ACM Transactions on Graphics 25, 3 (July 2006), 987--995.
24. S. M. Kay. 1988. Modern Spectral Estimation: Theory and Application. Prentice Hall.
25. D. Komatitsch, G. Erlebacher, D. Göddeke, and D. Michéa. 2010. High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster. Journal of computational physics 229, 20 (2010), 7692--7714.
26. T. R. Langlois, S. S. An, K. K. Jin, and D. L. James. 2014. Eigenmode Compression for Modal Sound Models. ACM Transactions on Graphics (TOG) 33, 4, Article 40 (July 2014), 9 pages.
27. T. R. Langlois, C. Zheng, and D. L. James. 2016. Toward Animating Water with Complex Acoustic Bubbles. ACM Transactions on Graphics (TOG) 35, 4, Article 95 (July 2016), 13 pages.
28. D. Li, Y. Fei, and C. Zheng. 2015. Interactive Acoustic Transfer Approximation for Modal Sound. ACM Transactions on Graphics (TOG) 35, 1 (2015).
29. Q.-H. Liu and J. Tao. 1997. The perfectly matched layer for acoustic waves in absorptive media. The Journal of the Acoustical Society of America 102, 4 (1997), 2072--2082.
30. Y. J. Liu. 2009. Fast Multipole Boundary Element Method: Theory and Applications in Engineering. Cambridge University Press, Cambridge.
31. P. J. Looges and S. Olariu. 1992. Optimal greedy algorithms for indifference graphs. In Proceedings IEEE Southeastcon '92. 144--149 vol. 1.
32. R. Mehra, N. Raghuvanshi, L. Savioja, M. C. Lin, and D. Manocha. 2012. An efficient GPU-based time domain solver for the acoustic wave equation. Applied Acoustics 73, 2 (2012), 83 -- 94.
33. A. Meshram, R. Mehra, H. Yang, E. Dunn, J.-M. Frahm, and D. Manochak. 2014. P-hrtf: Efficient personalized hrtf computation for high-fidelity spatial sound. Mixed and Augmented Reality (ISMAR), 2014 IEEE International Symposium on (2014).
34. P. Micikevicius. 2009. 3D Finite Difference Computation on GPUs Using CUDA. In Proceedings of 2Nd Workshop on General Purpose Processing on Graphics Processing Units (GPGPU-2). ACM, New York, NY, USA, 79--84.
35. J. D. Morrison and J.-M. Adrien. 1993. Mosaic: A framework for modal synthesis. Computer Music Journal 17, 1 (1993), 45--56.
36. J. F. O'Brien, C. Shen, and C. M. Gatchalian. 2002. Synthesizing sounds from rigid-body simulations. In The ACM SIGGRAPH 2002 Symposium on Computer Animation. ACM Press, 175--181.
37. D. K. Pai, K. van den Doel, D. L. James, J. Lang, J. E. Lloyd, J. L. Richmond, and S. H. Yau. 2001. Scanning physical interaction behavior of 3D objects. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques. ACM, 87--96.
38. S. Prepelita, M. Geronazzo, F. Avanzini, and L. Savioja. 2016. Influence of voxelization on finite difference time domain simulations of head-related transfer functions. The Journal of the Acoustical Society of America 139, 5 (2016), 2489--2504.
39. Z. Ren, H. Yeh, and M. C. Lin. 2013. Example-guided physically based modal sound synthesis. ACM Transactions on Graphics (TOG) 32, 1 (2013), 1.
40. Y. Saad and M. H. Schultz. 1986. GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM J. Sci. Statist. Comput. 7, 3 (July 1986), 856--869.
41. X. Serra and J. Smith. 1990. Spectral modeling synthesis: A sound analysis/synthesis system based on a deterministic plus stochastic decomposition. Computer Music Journal 14, 4 (1990), 12--24.
42. A. A. Shabana. 2012. Theory of Vibration: An Introduction. Springer Science & Business Media.
43. A. A. Shabana. 2013. Dynamics of multibody systems. Cambridge university press.
44. W. Śmigaj, T. Betcke, S. Arridge, J. Phillips, and M. Schweiger. 2015. Solving Boundary Integral Problems with BEM++. ACM Trans. Math. Software 41, 2, Article 6 (Feb. 2015), 40 pages.
45. A. Taflove and S. C. Hagness. 2005. Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House.
46. T. Takala and J. Hahn. 1992. Sound rendering. In ACM Transactions on Graphics (Proceedings of SIGGRAPH 1992). 211--220.
47. K. van den Doel, P. G. Kry, and D. K. Pai. 2001. FoleyAutomatic: Physically-based Sound Effects for Interactive Simulation and Animation. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM Transactions on Graphics (Proceedings of SIGGRAPH 2001)). ACM, New York, NY, USA, 537--544.
48. K. van den Doel and D. K. Pai. 1996. Synthesis of shape dependent sounds with physical modeling. International Conference on Auditory Display 28 (1996).
49. O. von Estorff. 2000. Boundary Elements in Acoustics: Advances and Applications. WIT Press, Southhampton, UK.
50. J.-H. Wang, A. Qu, T. R. Langlois, and D. L. James. 2018. Toward Wave-based Sound Synthesis for Computer Animation. ACM Transactions on Graphics (TOG) 37, 4, Article 109 (July 2018), 16 pages.
51. Wikipedia. 2019. All-interval twelve-tone row. https://en.wikipedia.org/wiki/All-interval_twelve-tone_row
52. T. W Wu. 2000. Boundary Element Acoustics: Fundamentals and Computer Codes. WIT Press, Southhampton, UK.
53. C. Zheng and D. L. James. 2009. Harmonic Fluids. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2009) 28, 3 (Aug. 2009).
54. C. Zheng and D. L. James. 2010. Rigid-Body Fracture Sound with Precomputed Soundbanks. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2010) 29, 3 (July 2010).
55. C. Zheng and D. L. James. 2011. Toward High-Quality Modal Contact Sound. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2011) 30, 4 (Aug. 2011).
56. E. Zwicker and H. Fastl. 2013. Psychoacoustics: Facts and models. Vol. 22. Springer Science & Business Media.

Index Terms

• Computing methodologies

  • Computer graphics

    • Animation

      • Physical simulation

  • Modeling and simulation