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Fast Time-Domain Edge-Diffraction Calculations for Interactive Acoustic Simulations


The inclusion of edge diffraction has long been recognized as an improvement to geometrical-acoustics (GA) modeling techniques, particularly for acoustic simulations of complex environments that are represented as collections of finite-sized planar surfaces. One particular benefit of combining edge diffraction with GA components is that the resulting total sound field is continuous when an acoustic source or receiver crosses a specular-zone or shadow-zone boundary, despite the discontinuity experienced by the associated GA component. In interactive acoustic simulations which include only GA components, such discontinuities may be heard as clicks or other undesirable audible artifacts, and thus diffraction calculations are important for high perceptual quality as well as physical realism. While exact diffraction calculations are difficult to compute at interactive rates, approximate calculations are possible and sufficient for situations in which the ultimate goal is a perceptually plausible simulation rather than a numerically exact one. In this paper, we describe an edge-subdivision strategy that allows for fast time-domain edge-diffraction calculations with relatively low error when compared with results from a more numerically accurate solution. The tradeoff between computation time and accuracy can be controlled with a number of parameters, allowing the user to choose the speed that is necessary and the error that is tolerable for a specific modeling scenario.


  1. 1.

    Vanderkooy J: A simple theory of cabinet edge diffraction. Journal of the Audio Engineering Society 1991,39(12):923–933.

    Google Scholar 

  2. 2.

    Menounou P, You JH: Experimental study of the diffracted sound field around jagged edge noise barriers. The Journal of the Acoustical Society of America 2004,116(5):2843–2854. 10.1121/1.1804633

    Article  Google Scholar 

  3. 3.

    Torres RR, Svensson UP, Kleiner M: Computation of edge diffraction for more accurate room acoustics auralization. The Journal of the Acoustical Society of America 2001,109(2):600–610. 10.1121/1.1340647

    Article  Google Scholar 

  4. 4.

    Funkhouser T, Tsingos N, Carlbom I, et al.: A beam tracing method for interactive architectural acoustics. The Journal of the Acoustical Society of America 2004,115(2):739–756. 10.1121/1.1641020

    Article  Google Scholar 

  5. 5.

    Antonacci F, Foco M, Sarti A, Tubaro S: Fast modeling of acoustic reflections and diffraction in complex environments using visibility diagrams. Proceedings of 12th European Signal Processing Conference (EUSIPCO '04), September 2004, Vienna, Austria 1773–1776.

    Google Scholar 

  6. 6.

    Kouyoumjian RG, Pathak PH: A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface. Proceedings of the IEEE 1974, 62: 1448–1461.

    Article  Google Scholar 

  7. 7.

    Biot MA, Tolstoy I: Formulation of wave propagation in infinite media by normal coordinates with an application to diffraction. The Journal of the Acoustical Society of America 1957,29(3):381–391. 10.1121/1.1908899

    Article  Google Scholar 

  8. 8.

    Medwin H: Shadowing by finite noise barriers. The Journal of the Acoustical Society of America 1981,69(4):1060–1064. 10.1121/1.385684

    Article  Google Scholar 

  9. 9.

    Svensson UP, Fred RI, Vanderkooy J: An analytic secondary source model of edge diffraction impulse responses. The Journal of the Acoustical Society of America 1999,106(5):2331–2344 . 10.1121/1.428071

    Article  Google Scholar 

  10. 10.

    Calamia PT, Svensson UP: Edge subdivision for fast diffraction calculations. Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, October 2005, New Paltz, NY, USA 187–190.

    Google Scholar 

  11. 11.

    Allen JB, Berkley DA: Image method for efficiently simulating small-room acoustics. The Journal of the Acoustical Society of America 1979,65(4):943–950. 10.1121/1.382599

    Article  Google Scholar 

  12. 12.

    Borish J: Extension of the image model to arbitrary polyhedra. The Journal of the Acoustical Society of America 1984,75(6):1827–1836. 10.1121/1.390983

    Article  Google Scholar 

  13. 13.

    Krokstad A, Strøm S, Sørsdal S: Calculating the acoustical room response by the use of a ray tracing technique. Journal of Sound and Vibration 1968,8(1):118–125. 10.1016/0022-460X(68)90198-3

    Article  Google Scholar 

  14. 14.

    Funkhouser T, Carlbom I, Elko G, Pingali G, Sondhi M, West J: A beam tracing approach to acoustic modeling for interactive virtual environments. Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '98), July 1998, Orlando, Fla, USA 21–32.

    Google Scholar 

  15. 15.

    Keller JB: Geometrical theory of diffraction. Journal of the Optical Society of America 1962,52(2):116–130. 10.1364/JOSA.52.000116

    MathSciNet  Article  Google Scholar 

  16. 16.

    Tsingos N, Funkhouser T, Ngan A, Carlbom I: Modeling acoustics in virtual environments using the uniform theory of diffraction. Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '01), August 2001, Los Angeles, Calif, USA 545–552.

    Google Scholar 

  17. 17.

    Antonacci F, Foco M, Sarti A, Tubaro S: Accurate and fast audio-realistic rendering of sounds in virtual environments. Proceedings of 6th IEEE Workshop on Multimedia Signal Processing, September–October 2004, Siena, Italy 271–274.

    Google Scholar 

  18. 18.

    Antonacci F, Foco M, Sarti A, Tubaro S: Real time modeling of acoustic propagation in complex environments. Proceedings of 7th International Conference on Digital Audio Effects (DAFx '04), October 2004, Naples, Italy 274–279.

    Google Scholar 

  19. 19.

    Medwin H, Childs E, Jebsen GM: Impulse studies of double diffraction: a discrete Huygens interpretation. The Journal of the Acoustical Society of America 1982,72(3):1005–1013. 10.1121/1.388231

    Article  Google Scholar 

  20. 20.

    Pulkki V, Lokki T, Savioja L: Implementation and visualization of edge diffraction with image-source method. Proceedings of 112th Audio Engineering Society Convention, May 2002, Munich, Germany

    Google Scholar 

  21. 21.

    Calamia PT, Svensson UP, Funkhouser T: Integration of edge-diffraction calculations and geometrical-acoustics modeling. Proceedings of Forum Acusticum, August 2005, Budapest, Hungary 2499–2504.

    Google Scholar 

  22. 22.

    Lokki T, Svensson UP, Savioja L: An efficient auralization of edge diffraction. Proceedings of the Audio Engineering Society 21st International Conference on Architectural Acoustics and Sound Reinforcement, June 2002, St. Petersburg, Russia 166–172.

    Google Scholar 

  23. 23.

    Savioja L, Huopaniemi J, Lokki T, Väänänen R: Creating interactive virtual acoustic environments. Journal of the Audio Engineering Society 1999,47(9):675–705.

    Google Scholar 

  24. 24.

    Savioja L, Huopaniemi J, Lokki T: Auralization applying the parametric room acoustic modeling technique-the DIVA auralization system. Proceedings of the 8th International Conference on Auditory Display, July 2002, Kyoto, Japan

    Google Scholar 

  25. 25.

    de Rycker N: Theoretical and numerical study of sound diffraction-application to room acoustics auralization. In Rapport de Stage D'Option Scientifique. Ècole Polytechnique, Paris, France; 2002.

    Google Scholar 

  26. 26.

    Torres R, de Rycker N, Kleiner M: Edge diffraction and surface scattering in concert halls: physical and perceptual aspects. Journal of Temporal Design in Architecture and the Environment 2004, 4: 52–58.

    Google Scholar 

  27. 27.

    Dalenbäck B-I: CATT-Acoustic v8 Manual.

  28. 28.

    Christensen CL: ODEON Room Acoustics Program ver. 8 Manual.

  29. 29.

    Tsingos N, Gascuel J-D: Soundtracks for computer animation: sound rendering in dynamic environments with occlusions. Proceedings of the Conference on Graphics Interface, May 1997, Kelowna, British Columbia, Canada 9–16.

    Google Scholar 

  30. 30.

    Tsingos N, Gascuel J-D: Fast rendering of sound occlusion and diffraction effects for virtual acoustic environments. Proceedings of the Audio Engineering Society 104th Convention, May 1998, Amsterdam, The Netherlands preprint no. 4699

    Google Scholar 

  31. 31.

    Svensson UP, Calamia PT: Edge-diffraction impulse responses near specular-zone and shadow-zone boundaries. Acta Acustica united with Acustica 2006,92(4):501–512.

    Google Scholar 

  32. 32.

    Clay CS, Kinney WA: Numerical computations of time-domain diffractions from wedges and reflections from facets. The Journal of the Acoustical Society of America 1988,83(6):2126–2133. 10.1121/1.396393

    Article  Google Scholar 

  33. 33.

    Davis PJ, Rabinowitz P: Methods of Numerical Integration. 2nd edition. Academic Press, New York, NY, USA; 1984.

    Google Scholar 

  34. 34.

    Torres R: Studies of edge diffraction and scattering: applications to room acoustics and auralization, Ph.D. thesis. Chalmers University of Technology, Göteborg, Sweden; 2000.

    Google Scholar 

  35. 35.

    Lokki T, Pulkki V: Measurement and theoretical validation of diffraction from a single edge. Proceedings of the 18th International Congress on Acoustics (ICA '04), April 2004, Kyoto, Japan 2: 929–932.

    Google Scholar 

  36. 36.

    Løvstad A, Svensson UP: Diffracted sound field from an orchestra pit. Acoustical Science and Technology 2005,26(2):237–239. 10.1250/ast.26.237

    Article  Google Scholar 

  37. 37.

    Davis AMJ, Scharstein RW: The complete extension of the Biot-Tolstoy solution to the density contrast wedge with sample calculations. The Journal of the Acoustical Society of America 1997,101(4):1821–1835. 10.1121/1.418220

    Article  Google Scholar 

  38. 38.

    Novarini JC, Keiffer RS: Impulse response of a density contrast wedge: practical implementation and some aspects of its diffracted component. Applied Acoustics 1999,58(2):195–210. 10.1016/S0003-682X(98)00054-1

    Article  Google Scholar 

  39. 39.

    Svensson UP, Calamia PT: The use of edge diffraction in computational room acoustics. The Journal of the Acoustical Society of America 2006, 120: 2998. (A)

    Article  Google Scholar 

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Correspondence to Paul T Calamia.

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Calamia, P.T., Svensson, U.P. Fast Time-Domain Edge-Diffraction Calculations for Interactive Acoustic Simulations. EURASIP J. Adv. Signal Process. 2007, 063560 (2006).

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  • Planar Surface
  • Complex Environment
  • Physical Realism
  • Accurate Solution
  • Approximate Calculation