comparative visualization for wave-based and geometric acoustics eduard deines 1, martin bertram 3,...
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![Page 1: Comparative Visualization for Wave-based and Geometric Acoustics Eduard Deines 1, Martin Bertram 3, Jan Mohring 4, Jevgenij Jegorovs 4, Frank Michel 1,](https://reader035.vdocument.in/reader035/viewer/2022062618/5514ebee550346b0338b5d8d/html5/thumbnails/1.jpg)
Comparative Visualization for Wave-based and Geometric AcousticsEduard Deines1, Martin Bertram3, Jan Mohring4, Jevgenij Jegorovs4, Frank Michel1, Hans Hagen2, and Gregory M. Nielson5
1IRTG Kaiserslautern2University of Kaiserslautern3DFKI Kaiserslautern
4ITWM Kaiserslautern5Arizona State University
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Comparative Visualization for Wave-based and Geometric Acoustics
2Overview
• Motivation
• Acoustic Simulation• Modified Phonon Tracing• FEM-based solver
• Comparison approach• Interference pattern visualization• Gain visualization
![Page 3: Comparative Visualization for Wave-based and Geometric Acoustics Eduard Deines 1, Martin Bertram 3, Jan Mohring 4, Jevgenij Jegorovs 4, Frank Michel 1,](https://reader035.vdocument.in/reader035/viewer/2022062618/5514ebee550346b0338b5d8d/html5/thumbnails/3.jpg)
Comparative Visualization for Wave-based and Geometric Acoustics
3Motivation
• Shortcomings of geometric and wave-based methods
• Combination of both approaches
• Numerical and visual comparison
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Comparative Visualization for Wave-based and Geometric Acoustics
4Previous Work
• Phonon tracing, based on sound particles
• Computation of energy decomposition for each phonon (phonon emission)
• Construction of response filters for each listener position (phonon collection)
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Comparative Visualization for Wave-based and Geometric Acoustics
5Previous Work
Scattered data
Listener based
SurfacesSingle particle
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Comparative Visualization for Wave-based and Geometric Acoustics
6Overview
• Motivation
• Acoustic Simulation• Modified Phonon Tracing• FEM-based solver
• Comparison approach• Interference pattern visualization• Gain visualization
![Page 7: Comparative Visualization for Wave-based and Geometric Acoustics Eduard Deines 1, Martin Bertram 3, Jan Mohring 4, Jevgenij Jegorovs 4, Frank Michel 1,](https://reader035.vdocument.in/reader035/viewer/2022062618/5514ebee550346b0338b5d8d/html5/thumbnails/7.jpg)
Comparative Visualization for Wave-based and Geometric Acoustics
7Modified Phonon Tracing
• Modeling linear pressure attenuation by Gaussian basis functions dilated proportional with traversed distance => approximates partition of unity for the basis functions
• Tracing pressure rather then energy => better comparison with FEM
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Comparative Visualization for Wave-based and Geometric Acoustics
8Phonon Emission
• For each phonon:• Pressure spectrum• Virtual source• Phonon’s current
position
• One emmission, multiple collection passes for different listeners
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Comparative Visualization for Wave-based and Geometric Acoustics
9Phonon Emission
• Reflection at scene elements• Update virtual source• Multiply pressure by
• Re-use path by next phonons• Record phonons on scene
elements
• Emission according to source distribution
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Comparative Visualization for Wave-based and Geometric Acoustics
10Phonon Collection
• For each visible phonon:• Add unit pulse translated by
distance• Scaling decreases with:
Accumulated length Wall absorption
• Scaling depends on: Phonon outgoing direction Direction from virtual source to
listener position
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Comparative Visualization for Wave-based and Geometric Acoustics
11Phonon Collection
• Scaling depends on:• Reference pressure at 1m from
source• Gaussian weighting function
• split unit pulse into frequency bands
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Comparative Visualization for Wave-based and Geometric Acoustics
12Overview
• Motivation
• Acoustic Simulation• Modified Phonon Tracing• FEM-based solver
• Comparison approach• Interference pattern visualization• Gain visualization
![Page 13: Comparative Visualization for Wave-based and Geometric Acoustics Eduard Deines 1, Martin Bertram 3, Jan Mohring 4, Jevgenij Jegorovs 4, Frank Michel 1,](https://reader035.vdocument.in/reader035/viewer/2022062618/5514ebee550346b0338b5d8d/html5/thumbnails/13.jpg)
Comparative Visualization for Wave-based and Geometric Acoustics
13Finite Element Method (FEM)
• Solving wave equation by FEM
• FEM approximates the wave equation by a large system of ODEs
• To many unknowns to solve the ODEs => reduction needed
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Comparative Visualization for Wave-based and Geometric Acoustics
14Finite Element Method (FEM)
• Representation of the system dynamics by a superposition of eigenmodes
• The coefficients of the eigenmodes are the unknowns of the reduced system
• Samplewise constant input => transformation of the continuous state-space model into a discrete one
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Comparative Visualization for Wave-based and Geometric Acoustics
15Finite Element Method (FEM)
• Typically few hundred unknowns rather than 10,000 degrees of freedom
• Required number of unknowns increases as the third power of the frequency => only for low-frequency bands
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Comparative Visualization for Wave-based and Geometric Acoustics
16Overview
• Motivation
• Acoustic Simulation• Modified Phonon Tracing• FEM-based solver
• Comparison approach• Interference pattern visualization• Gain visualization
![Page 17: Comparative Visualization for Wave-based and Geometric Acoustics Eduard Deines 1, Martin Bertram 3, Jan Mohring 4, Jevgenij Jegorovs 4, Frank Michel 1,](https://reader035.vdocument.in/reader035/viewer/2022062618/5514ebee550346b0338b5d8d/html5/thumbnails/17.jpg)
Comparative Visualization for Wave-based and Geometric Acoustics
17Test Scenario
Geometry Simulation scenario
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Comparative Visualization for Wave-based and Geometric Acoustics
18Simulation
• regular grid• wave number k = {3, 6, 9, 12, 15} f = {164.25, 328.5, 492.7, 657, 821.2} Hz• Phonon Tracing: point source, 100000 phonons• FEM: small membrane
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Comparative Visualization for Wave-based and Geometric Acoustics
19Overview
• Motivation
• Acoustic Simulation• Modified Phonon Tracing• FEM-based solver
• Comparison approach• Interference pattern visualization• Gain visualization
![Page 20: Comparative Visualization for Wave-based and Geometric Acoustics Eduard Deines 1, Martin Bertram 3, Jan Mohring 4, Jevgenij Jegorovs 4, Frank Michel 1,](https://reader035.vdocument.in/reader035/viewer/2022062618/5514ebee550346b0338b5d8d/html5/thumbnails/20.jpg)
Comparative Visualization for Wave-based and Geometric Acoustics
20Interference Pattern Visualization
• Color mapping:• Positive pressure to red• Negative pressure to blue• Reduction of saturation, depending on the
absolute pressure value• Mapping of pressure values below the
hearing threshold to gray
• Bilinear interpolation of color values for additional grid points
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Comparative Visualization for Wave-based and Geometric Acoustics
21Interference Pattern (k=6 / f=328.5 Hz)
FEM
Phonon Tracing
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Comparative Visualization for Wave-based and Geometric Acoustics
22Interference Pattern (k=12 / f=657 Hz)
FEM
Phonon Tracing
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Comparative Visualization for Wave-based and Geometric Acoustics
23Interference Pattern
k=6 k=6
k=12 k=12
FEM
Phonon Tracing
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Comparative Visualization for Wave-based and Geometric Acoustics
24Overview
• Motivation
• Acoustic Simulation• Modified Phonon Tracing• FEM-based solver
• Comparison approach• Interference pattern visualization• Gain visualization
![Page 25: Comparative Visualization for Wave-based and Geometric Acoustics Eduard Deines 1, Martin Bertram 3, Jan Mohring 4, Jevgenij Jegorovs 4, Frank Michel 1,](https://reader035.vdocument.in/reader035/viewer/2022062618/5514ebee550346b0338b5d8d/html5/thumbnails/25.jpg)
Comparative Visualization for Wave-based and Geometric Acoustics
25Gain Visualization
• Acoustic metric: influence of the room
• Error:
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Comparative Visualization for Wave-based and Geometric Acoustics
26Gain Visualization
• Color coding:• Use of HSV color space• Red for maximum value• Blue for minimum value
• Same range for different simulations
• Same range for all error plots
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Comparative Visualization for Wave-based and Geometric Acoustics
27Gain - Error
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Comparative Visualization for Wave-based and Geometric Acoustics
28Gain (k=3 / f=164.25 Hz)
FEM Phonon Tracing Error
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Comparative Visualization for Wave-based and Geometric Acoustics
29Gain (k=6 / f=328.5 Hz)
FEM Phonon Tracing Error
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Comparative Visualization for Wave-based and Geometric Acoustics
30Gain (k=12 / f=657 Hz)
FEM Phonon Tracing Error
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Comparative Visualization for Wave-based and Geometric Acoustics
31Acknowledgments
• Stiftung Rheinland-Pfalz fuer Innovation
• Kaiserslautern Excellence Cluster Dependable Adaptive Systems and Mathematical Modeling
• US Army Research Office
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Comparative Visualization for Wave-based and Geometric Acoustics
32
Thank you for attention!