comparative visualization for wave-based and geometric acoustics eduard deines 1, martin bertram 3,...
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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
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
Comparative Visualization for Wave-based and Geometric Acoustics
3Motivation
• Shortcomings of geometric and wave-based methods
• Combination of both approaches
• Numerical and visual comparison
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)
Comparative Visualization for Wave-based and Geometric Acoustics
5Previous Work
Scattered data
Listener based
SurfacesSingle particle
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
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
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
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
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
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
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
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
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
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
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
Comparative Visualization for Wave-based and Geometric Acoustics
17Test Scenario
Geometry Simulation scenario
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
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
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
Comparative Visualization for Wave-based and Geometric Acoustics
21Interference Pattern (k=6 / f=328.5 Hz)
FEM
Phonon Tracing
Comparative Visualization for Wave-based and Geometric Acoustics
22Interference Pattern (k=12 / f=657 Hz)
FEM
Phonon Tracing
Comparative Visualization for Wave-based and Geometric Acoustics
23Interference Pattern
k=6 k=6
k=12 k=12
FEM
Phonon Tracing
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
Comparative Visualization for Wave-based and Geometric Acoustics
25Gain Visualization
• Acoustic metric: influence of the room
• Error:
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
Comparative Visualization for Wave-based and Geometric Acoustics
27Gain - Error
Comparative Visualization for Wave-based and Geometric Acoustics
28Gain (k=3 / f=164.25 Hz)
FEM Phonon Tracing Error
Comparative Visualization for Wave-based and Geometric Acoustics
29Gain (k=6 / f=328.5 Hz)
FEM Phonon Tracing Error
Comparative Visualization for Wave-based and Geometric Acoustics
30Gain (k=12 / f=657 Hz)
FEM Phonon Tracing Error
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
Comparative Visualization for Wave-based and Geometric Acoustics
32
Thank you for attention!