Beam Tracing with Refraction

Open access

Abstract

This paper presents the beam tracing with refraction method, developed to examine the possibility of creating the beam tracing simulation of sound propagation in environments with piecewise non- homogenous media. The beam tracing with refraction method (BTR) is developed as an adaptive beam tracing method that simulates not only the reflection but also the refraction of sound. The scattering and the diffraction of sound are not simulated. The BTR employs 2D and 3D topology in order to efficiently simulate scenes containing non-convex media. After the beam tracing is done all beams are stored in a beam tree and kept in the computer memory. The level of sound intensity at the beginning of each beam is also memorized. This beam data structure enables fast recalculation of results for stationary source and geometry. The BTR was compared with two commercial ray tracing simulations, to check the speed of BTR algorithms. This comparison demonstrated that the BTR has a performance similar to state-of- the-art room-acoustics simulations. To check the ability to simulate refraction, the BTR was compared with a commercial Finite Elements Method (FEM) simulation. In this comparison the BTR simulated the focusing of the ultrasound with an acoustic lens, with good accuracy and excellent performance.

1. Alpkocak A., Sis M.K. (2010), Computing im-pulse response of room acoustics using the ray-tracingmethod in time domain, Archives of Acoustics, 35, 4, 505-519.

2. Bork I. (2005), Report on the 3rd Round Robin onRoom Acoustical Computer Simulation - Part II: Cal-culations, Acta Acustica united with Acustica, 91, 753-763.

3. Botteldooren D. (1994), Acoustical ?nite-differencetime-domain simulations in a quasi-Cartesian grid, Journal of Acoustical Society of America, 95, 2313-2319.

4. James A., Dalenback B.I., Naqvi A. (2008), Com-puter Modelling With CATT Acoustics - Theory andPractise of Diffuse Reflection and Array Modeling, Pro- ceedings of 24th Reproduced Sound Conference, 20-21.11, Brighton, UK.

5. Drumm I. (2000), The adaptive beam tracing algo-rithm, Journal of Acoustical Society of America, 107, 3, 1405-1412.

6. Farina A. (1994), Ramsete un nuovo software per laprevisione del campo sonoro in teatri, ambienti indus-triali ed ambiente esterno, Atti del XXII Congresso Nazionale AIA, 13-15 April, Lecce.

7. Farina A. (2000), Validation of the pyramid tracingalgorithm for sound propagation outdoors: comparisonwith experimental measurements and with the ISO/DIS9613 standards, Advances in Engineering Software, 31, 4, 241-250.

8. Feistel S., Ahnert W., Miron A., Schmitz O. (2007), Improved methods for calculating room impulseresponse with EASE 4.2 AURA, Proceedings of 19th International congress on Acoustics, 2-7 September, Madrid.

9. Fink K. (1994), Computer Simulation of PressureFields Generated by Acoustic Lens Beamformers, M.Sc. Thesis, University of Washington.

10. Funkhouser T., Carlbom I., Elko G., Pingali G., Sondhi M., West J.A. (1998), Beam Tracing Ap-proach to Acoustic Modeling for Interactive Virtual En-vironments, Proceedings SIGGRAPH 98, pp. 21-32, Orlando.

11. Goldberg D. (1991), What every computer scien-tist should know about floating-point arithmetic, ACM Computing Surveys, 21, 1, 5-48.

12. Heckbert P.S., Hanrahan P. (1984), Beam Trac-ing Polygonal Objects, Proceedings of the 11th annual conference on Computer graphics and interactive tech- niques, pp. 119-127, New York.

13. Kleiner M., Dalenback B.I., Svensson P. (1993), Auralization - An Overview, Journal of Audio Engi- neering Society, 41, 11, 861-875.

14. Laine S., Siltanen S., Lokki T., Savioja L. (2009), Accelerated beam tracing algorithm, Applied Acoustics (Elsevier), 70, 1, 172-181.

15. Lewers T. (1993), A combined beam tracing and ra-diant exchange computer model of room acoustics, Ap- plied Acoustics (Elsevier), 38, 2, 161-178.

16. Maercke D., Maercke D., Martin J. (1993), Theprediction of echograms and impulse responses withinthe Epidaure software, Applied Acoustics (Elsevier), 38, 2, 93-114.

17. Noisternig M., Katz B.F.G, Siltanen S., Savioja L. (2008), Framework for Real-Time Auralization inArchitectural Acoustics, Acta Acustica united with Acustica, 94, 1000-1015.

18. Picaut J., Polack J.-D., Simon L. (1997), A Math-ematical Model of Diffuse Sound Field Based on a Dif-fusion Equation, Acta Acustica united with Acustica, 83, 614-621.

19. Pierce A.D. (1981), Acoustics - An Introduction toits Physical Principles and Applications, McGraw-Hill.

20. Shah M., Pattanaik S. (2007), Caustic Mapping: AnImage-space Technique for Real-time Caustics, IEEE Transactions on Visualization and Computer Graphics, 13, 272-280.

21. Sikora M., Mateljan I., Bogunović N. (2010), Theeffect of refraction as a non-linear transformation onbeam tracing simulation of sound propagation, Pro- ceedings of 1st EAA EUROREGIO Congress on Sound and Vibration - Acta Acustica united with Acustica, 96, Supp. 1, 62.

22. Siltanen S., Lokki T., Kiminki S., Savioja L. (2007), The room acoustic rendering equation, Journal of Acoustical Society of America, 95, 2313-2319, 122, 3, 1624-1635.

23. Siltanen S., Lokki T., Savioja L. (2009), FrequencyDomain Acoustic Radiance Transfer for Real-Time Au-ralization, Acta Acustica united with Acustica, 95, 106-117.

24. Sutherland I.E., Hodgman G.W. (1974), Reentrantpolygon clipping, Communications of the ACM, 17, 1, pp. 32-42.

25. Stephenson U. (1996), Quantized Pyramidal BeamTracing - a new algorithm for room acoustics and noiseimmission prognosis, Acta Acustica united with Acus- tica, 82, 517-525.

26. Tsingos N., Funkhouser T. (2001), Modeling Acous-tics in Virtual Environments Using 1the Uniform The-ory of Diffraction, Proceedings of ACM SIGGRAPH 2001, pp. 545-552, Los Angeles.

27. Vorlander M. (2008), Auralization, Springer.

28. Walsh J.P., Dadoun N., Kirkpatrick D.G. (1985), The geometry of beam tracing, Proceedings of the first annual symposium on Computational geometry, pp. 55-61, Toronto.

29. Wojcik G.L., Vaughan D.K., Murray V., Mould J. Jr. (1994), Time-domain Modeling of CompositeArrays for Underground Imaging, Proceedings of the IEEE Ultrasonics Symposium, pp. 1027-1032, Cannes.

30. Wojcik G.L., Vaughan D.K., Abboud N., Mould J. Jr. (1998), Finite Element Modeling for UltrasonicTransducers, Proceedings of Ultrasonic transducer en- gineering Conference, pp. 19-42, San Diego.

Archives of Acoustics

The Journal of Institute of Fundamental Technological of Polish Academy of Sciences

Journal Information


IMPACT FACTOR 2016: 0.816
5-year IMPACT FACTOR: 0.835

CiteScore 2016: 1.15

SCImago Journal Rank (SJR) 2016: 0.432
Source Normalized Impact per Paper (SNIP) 2016: 0.948

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 164 123 10
PDF Downloads 71 60 5