comparative visualization for wave-based and geometric acoustics

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!