An Introduction to Sound
Rendering
ANISH CHANDAK
ACHANDAK@CS.UNC.EDU
COMP 770 (SPRING’09)
© Copyright 2009 Anish Chandak
Sound Rendering: An Overview
Scientific Visualization
Acoustic Geometry
-- surface simplification
Acoustic Material
-- absorption coefficient
-- scattering coefficient
Source Modeling
-- area source
-- emitting characteristics
-- sound signal
Modeling
© Copyright 2009 Anish Chandak
Specular Reflection
Scattering
Diffraction
Refraction
Doppler Effect
Attenuation
Propagation
Late Reverberation
Personalized HRTFs
for 3D sound
Digital Signal Processing
Interpolation for
Dynamic Scenes
Rendering
(Sweet Audio!)
Sound Rendering: An Overview
Scientific Visualization
Acoustic Geometry
-- surface simplification
Acoustic Material
-- absorption coefficient
-- scattering coefficient
Source Modeling
-- area source
-- emitting characteristics
-- sound signal
Modeling
© Copyright 2009 Anish Chandak
Specular Reflection
Scattering
Diffraction
Refraction
Doppler Effect
Attenuation
Propagation
Late Reverberation
Personalized HRTFs
for 3D sound
Digital Signal Processing
Interpolation for
Dynamic Scenes
Rendering
(Sweet Audio!)
Applications
 Advanced Interfaces
 Multi-sensory Visualization
Minority Report (2002)
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Multi-variate Data
Visualization
Applications
 Games
 VR Training
Game (Half-Life 2)
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Medical Personnel Training
Applications
 Acoustic Prototyping
Symphony Hall, Boston
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Level Editor, Half Life
Modeling
Acoustics vs. Graphics
Acoustic Geometry
-- surface simplification
Acoustic Material
-- absorption coefficient
-- scattering coefficient
Source Modeling
-- area source
-- emitting characteristics
-- sound signal
Modeling
© Copyright 2009 Anish Chandak
 Low geometric details
vs. High geometric
details
Propagation
Acoustics vs. Graphics
 343 m/s vs.
Specular Reflection
Scattering
Diffraction
Refraction
Doppler Effect
Attenuation
Propagation
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300,000,000 m/s
 20 to 20K Hz vs. RGB
 17 m to 17 cm vs. 700
to 400 nm
Rendering
Acoustics vs. Graphics
Late Reverberation
Personalized HRTFs
for 3D sound
Digital Signal Processing
Interpolation for
Dynamic Scenes
Rendering
(Sweet Audio!)
© Copyright 2009 Anish Chandak
 Compute intensive DSP
vs. Simple addition of
colors
 44.1 KHz vs. 30 Hz
 Psychoacoustics vs.
Visual psychophysics
Sound Propagation in Games
 Strict time budget for audio simulations
 Games are dynamic
 Moving sound sources
 Moving listeners
 Moving scene geometry
 Trade-off speed with the accuracy of the simulation
 Static environment effects (assigned to regions in the scene)
© Copyright 2009 Anish Chandak
Sound Propagation Approaches
 Numerical Methods

Solve Helmholtz Wave Equation
Accurate
 Compute intensive (fourth power of frequency)
 Independent of model complexity


Methods: FEM, BEM, FDTD, DWM
 Geometric Methods

Ray-Approximation of Wave Equation
High-frequency approximation
 Fast
 Dependent on model complexity


Methods: Image Source/Beam Tracing, Frustum Tracing, Ray
Tracing/Phonon Tracing
© Copyright 2009 Anish Chandak
Beam Tracing for Sound Propagation
 [Funkhouser,1998]
 Demo
 Input: point sound source, point listener, scene
geometry with acoustic properties
 Output: pressure impulse response (IR)
 Rendering: convolve IR with audio
signal of sound source
 Note: audio signal is a function of pressure
© Copyright 2009 Anish Chandak
Beam Tracing for Sound Propagation
Acoustic Geometry
-- surface simplification
Acoustic Material
Source Modeling
-- area source
-- emitting characteristics
-- sound signal
Propagation
-- absorption coefficient
-- scattering coefficient
Late Reverberation
Personalized HRTFs
for 3D sound
Digital Signal Processing
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Input
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Step 1 (pre-processing)
Spatial Subdivision
 Partition 3D space into convex regions (BSP Tree).
 Build adjacency graph.
[Wikipedia, Binary space partitioning]
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Step 1
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Step 2 (pre-processing)
Beam Tracing
 Compute Beam Tree
 Node Information





Cell ID
Beam and its apex
Cell boundary
Parent node ID
Attenuation
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Example: Step 2
[Funkhouser,1998]
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Example: Step 2
[Funkhouser,1998]
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Example: Step 2
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Step 2
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Step 2
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Step 2
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Step 2
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Step 2
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Step 3 (interactive)
Path Generation
 Find cell, C, containing





listener (log N)
For each beam in C check
for listener is inside it
Yes, then a path exist
Attenuation, path length,
and direction can be
computed quickly
Construct path by
traversing the beam tree
Compute Impulse
Response (IR)
© Copyright 2009 Anish Chandak
Example: Step 3
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Step 3
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Example: Step 3
[Funkhouser,1998]
© Copyright 2009 Anish Chandak
Step 4 (interactive)
Auralization
 Convolve IR with input sound signal
 Use the directional paths to simulate 3D audio using
HRTFs
*
Impulse Response (IR) * Sound Signal
© Copyright 2009 Anish Chandak
=
=
Output Audio
Ray Tracing for Sound Propagation
 [Krokstad,1968] [Kulowski,1984]
 Input: spherical sound source, spherical listener,
scene geometry with acoustic properties
 Output: energy impulse response (IR)
 Rendering:


convert energy IR into pressure IR
convolve IR with audio signal of sound source
 Note: audio signal is a function of pressure
© Copyright 2009 Anish Chandak
Shoot Sound Rays
(Step 1)
Shoot Rays From Source
Sound Source
Listener
S
Scene Geometry
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L
Trace Sound Rays
(Step 2)
S
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L
Specular Reflection
(Step 3)
S
L
Based on Reflection Coefficient
• Annihilate Or Energy Based
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Diffuse Reflection
(Step 3)
Based on Scattering
Coefficient
• Annihilate or
Choose a random
direction
S
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L
Construct Energy Histogram
(Step 3)
S
L
Collect Rays at
the Listener
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Construct Pressure IR from Energy Histogram
(Step 4)
 To compute sound signal at a point add sound
pressure of all contributions
 Phase angles of pn and pm are different and for quite
a large number of components
[Kuttruff,2007]
© Copyright 2009 Anish Chandak
Auralization
(Step 4)
 Convolve IR with input sound signal
 Use the directional paths to simulate 3D audio using
HRTFs
*
Impulse Response (IR) * Sound Signal
© Copyright 2009 Anish Chandak
=
=
Output Audio
Advanced Topic: Acoustic Rendering Equation
 Equivalent to rendering equation in computer




graphics [Kajiya, 1986]
Time dependent equation
Typically solved in frequency space
Very recent development [Siltanen, 2007]
Lot of potential to apply graphics techniques of
rendering to acoustic rendering equation
© Copyright 2009 Anish Chandak
Advanced Topic: Acoustic Surface Simplification
Visual Geometry
[Vorländer,2007]
© Copyright 2009 Anish Chandak
Acoustic Geometry
Advanced Topic: HRTFs for 3D sound
Inter-aural Level Difference (ILD)
Inter-aural Time Difference (ITD)
HRTF = Head Related Transfer Function. Encodes ILD, ITD, and much more.
© Copyright 2009 Anish Chandak
COMP 770 Course Project Suggestions
 Sound + Visual (Parameterized Sound)


Integrating Sounds and Motions in Virtual Environments
(http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=289953&site=ehostlive)
Presence: Teleoperators & Virtual Environments (Journal)
(http://search.ebscohost.com/login.aspx?direct=true&db=aph&jid=VTE&site=ehost-live)
 Acoustic Radiosity Simulation


A modified radiosity algorithm for integrated visual and auditory rendering
(doi:10.1016/0097-8493(93)90112-M)
Samuel Siltanen, Tapio Lokki, and Lauri Savioja, “ACOUSTIC RADIANCE TRANSFER
METHOD,” in The 19th International Congress on Acoustics (ICA) (Madrid, 2007),
http://www.sea-acustica.es/WEB_ICA_07/fchrs/papers/rba-05-008.pdf.
 Building Evacuation Using Sound Cues


Virtual Acoustic Technology: Its Role in the Development of an Auditory Navigation Beacon
for Building Evacuation
Building Acoustics (Journal) (http://www.ingentaconnect.com/content/mscp/bac)
© Copyright 2009 Anish Chandak
Reading List
Rudolf Rabenstein, Oliver Schips, and Er Stenger, “Acoustic
rendering of buildings,” in In 5th International Conference on
Building Simulation, 1997, 8—10
2. Funkhouser, T., Carlbom, I., Elko, G., Pingali, G., Sondhi, M.,
and West, J. 1998. A beam tracing approach to acoustic
modeling for interactive virtual environments. In Proceedings
of the 25th Annual Conference on Computer Graphics and
interactive Techniques SIGGRAPH '98. ACM, New York, NY,
21-32.
3. Peter Svensson, "The Early History of Ray Tracing in Room
Acoustics".
4. Funkhouser, Thomas and Tsingos, Nicolas and Jot, Jean-Marc,
"Survey of Methods for Modeling Sound Propagation in
Interactive Virtual Environment Systems," Presence and
Teleoperation, 2003.
1.
© Copyright 2009 Anish Chandak
Additional References
 Michael Vorländer, Auralization: Fundamentals of Acoustics,





Modelling, Simulation, Algorithms and Acoustic Virtual Reality,
2007.
Samuel Siltanen et al., “The room acoustic rendering equation,”
The Journal of the Acoustical Society of America 122, no. 3
(2007): 1624-1635, doi:10.1121/1.2766781.
Kajiya, J. T. 1986. The rendering equation. In Proceedings of the
13th Annual Conference on Computer Graphics and interactive
Techniques D. C. Evans and R. J. Athay, Eds. SIGGRAPH '86.
U. Krockstadt. Calculating the acoustical room response by the
use of a ray tracing technique. Journal of Sound and Vibrations,
8(18):118-125, 1968.
U. Kulowski. Algorithmic representation of the ray tracing
technique. Applied Acoustics, 18:449-469, 1984.
Heinrich Kuttruff, Acoustics, 2007.
© Copyright 2009 Anish Chandak
Questions?
© Copyright 2009 Anish Chandak
Modeling Sound Material
[Embrechts,2001] [Christensen,2005] [Tsingos,2007]
© Copyright 2009 Anish Chandak
Sound Source Modeling
Volumetric Sound Source
Directional Sound Source
Complex Vibration Source
© Copyright 2009 Anish Chandak