Interactive Sound Rendering

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Interactive Sound Rendering

• Session5 Simulating Diffraction
• Paul Calamia
• pcalamia_at_cs.princeton.edu

P. Calamia, M. Lin, D. Manocha, L. Savioja, N.
Tsingos
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Overview

• Motivation Why Diffraction?
• Simulation Methods
• Frequency Domain Uniform Theory of Diffraction
  (UTD)
• Time Domain Biot-Tolstoy-Medwin Formulation
  (BTM)
• Acceleration Techniques
• UTD Frequency Interpolation
• BTM Edge Subdivision
• Both Path Culling
• Implementation Example UTD with Frustum Tracing
• Additional Resources

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Motivation

• Wavelengths of audible sounds can be comparable
  to (or larger than) object dimensions so
  diffraction is an important acoustic propagation
  phenomenon
• Unlike wave-based simulation techniques,
  geometrical-acoustics (GA) techniques omit
  diffraction
• Incorrect reflection behavior from small surfaces
• No propagation around occluders / into shadow
  zones
• Sound-field discontinuities at reflection and
  shadow boundaries

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Continuity of Sound Fields with Diffraction

• Example reflection from a faceted arch with and
  without diffraction
• Even with low-resolution geometry, GA
  diffraction yields a continuous sound field

Images courtesy of Peter Svensson, NTNU
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Propagation into Shadow Zones

• Example propagation at a street crossing
• Diffraction from the corner allows propagation
  into areas without line of sight to the source

Images courtesy of Peter Svensson, NTNU
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Propagation into Shadow Zones

• Example propagation at a street crossing
• Diffraction from the corner allows propagation
  into areas without line of sight to the source
• Note the continuous wavefronts too

Images courtesy of Peter Svensson, NTNU
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Common Diffraction Methods

• Uniform Theory of Diffraction (UTD)
• Keller 62, Kouyoumjian and Pathak 74
• Typically used in the frequency domain although a
  time-domain formulation exists
• Assumptions
• Ideal wedge surfaces (perfectly rigid or soft)
• High frequency
• Infinitely long edges
• Far-field source and receiver
• For acoustic simulations see Tsingos et al. 01,
  Antonacci et al. 04, Taylor et al. 09

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Uniform Theory of Diffraction

• UTD gives the diffracted pressure as a function
  of incident pressure, distance attenuation, and a
  diffraction coefficient
• Angle of diffraction angle of incidence (?d
  ?i)
• Ray-like paths on a cone of diffraction

Images from Tsingos et al., 01
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Uniform Theory of Diffraction (UTD)
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Common Diffraction Methods

• Biot-Tolstoy-Medwin (BTM)
• Biot and Tolstoy 52, Medwin 81,
  Svensson et al. 99
• Typically used in the time domain although a
  frequency-domain formulation exists
• Assumptions
• Ideal wedge surfaces (perfectly rigid or soft)
• Point-source insonification
• For acoustic simulations see Torres et al. 01,
  Lokki et al. 02, Calamia et al. 07 and 08

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Biot-Tolstoy-Medwin Diffration (BTM)

• Wedge
• ?W exterior wedge angle
• ? p/?W is the wedge index
• Source and Receiver Edge-Aligned Cylindrical
  Coordinates (r,?, z)
• r radial distance from the edge
• ? angle measured from a face
• z distance along the edge
• Other
• m dist. from source to edge point
• l dist. from receiver to edge point
• A apex point, point of shortest path from S to
  R through the line containing the edge

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Biot-Tolstoy-Medwin Diffration (BTM)
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Numerical Challenge
Zone-Boundary Singularity

• Four terms in UTD and BTM
• When ?W gt p, two shadow boundaries and two
  reflection boundaries
• When ?W p, only reflection boundaries but
  inter-reflections (order 2, 3, ) are possible
• Each diffraction term is associated with a zone
  boundary
• Geometrical-acoustics sound field is
  discontinuous
• Diffracted field has a complimentary
  discontinuity to compensate

At the boundaries
BTM
UTD
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Numerical Challenge
Zone-Boundary Singularity
Reflection Boundary
Shadow Boundary
Source Position
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Numerical Challenge
Zone-Boundary Singularity
Normalized Amplitude
Reflection Boundary
Shadow Boundary
Source Position
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Numerical Challenge
Zone-Boundary Singularity

• Approximations exist to allow for numerically
  robust implementations
• BTM (Svensson and Calamia, Acustica 06) Serial
  expansion around the apex point
• UTD (Kouyoumjian and Pathak 74) Approximation
  valid in the neighborhood of the zone
  boundaries

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Acceleration Techniques

• Reduce computation for each diffraction component
• UTD Frequency Interpolation
• BTM Edge Subdivision
• Reduce the number of diffraction components
  through path culling
• Shadow Zone
• Zone-Boundary Proximity

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Frequency Interpolation

• Magnitude of diffraction transfer function
  typically is smooth
• Phase typically is linear
• Compute UTD coefficients at a limited number of
  frequencies (e.g. octave-band center frequencies
  63, 125, 250, , 8k, 16k Hz) and interpolate

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Edge Subdivision for Discrete-Time IRs

• Sample-aligned edge segments one for each IR
  sample
• Pros
• Accurate
• Good with approx for sample n0
• Cons
• Slow to compute
• Must be recalculated when S or R moves

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Edge Subdivision for Discrete-Time IRs

• Even edge segments
• Pros
• Trivial to compute
• Independent of S and R positions
• Cons
• No explicit boundaries for n0 ? harder to handle
  singularity
• Requires a scheme for multi-sample distribution

6.1
1.5
4.9
3.3
0.8
4.9
1.5
3.3
6.1
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Edge Subdivision for Discrete-Time IRs

• Hybrid Subdivision
• Use a small number of sample-aligned segments
  around the apex point
• High accuracy for the impulsive (high energy)
  onset
• Easy to use with approximations for h(n0)
• Use even segments for the rest of the edge
• Can be precomputed
• Limited recalculation for moving source or
  receiver

6.1
4.9
3.0
4.9
3.0
6.1
n2
n1
n1
n0
n2
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Hybrid Edge Subdivision Example

• 35 1.2 m x 1.2 m rigid panels
• Interpanel spacing 0.5 m
• 5 m above 2 source and 2 receiver positions
• Evaluate
• The number of sample-aligned segments 1 10
  
• The size of the even segments maximum sample
  span of 40, 100, and 300
• The numerical integration technique
• 1-Point (midpoint)
• 3-Point (Simpsons Rule)
• 5-Point (Compound Simpsons Rule with Romberg
  Extrapolation)

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Hybrid Edge Subdivision
S/R Zone Zone Segment Segment Norm. Max.
Pair Size Integ. Size Integ. Proc. Error
(samples) (samples) Time (dB)
1 4 1-point 100 1-point .0214 .97
1 all 5-point N/A N/A 1.0000 0
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Path Culling
Significant Growth in Paths Due to Diffraction
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Path Culling

• Option 1 For each wedge, compute diffraction
  only for paths in the shadow zone
• Intuition Sound field in the illuminated area
  around a wedge will be dominated by direct
  propagation and/or reflections, shadow zone will
  receive limited energy without diffraction
• Pro Allows propagation around obstacles
• Con Ignores GA discontinuity at reflection
  boundary
• Implementations described in Tsingos et al. 01,
  Antonacci et al. 04, Taylor et al. 09

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Path Culling

• Option 2 Compute diffraction only when amplitude
  is significant
• Intuition numerically/perceptually significant
  diffracted paths are those with highest amplitude
  and/or energy, typically those with the receiver
  close to a zone boundary
• Pro Eliminates large discontinuities in the
  simulated sound field
• Con Does not allow for propagation deep into
  shadow zones
• Implementation described in Calamia et al. 08

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Path Culling

• Significant variation in diffraction strength
  (220 dB in this example)

• Predict relative size based on proximity to a
  zone boundary and apex-point status

Reflection Boundary
Shadow Boundary
Source Position
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Path Culling Results

• Numerical and subjective evaluation in a simple
  concert-hall model

ABX tests comparing full IRs with culled IRs, 17
subjects
An angular threshold of 24 culls 92 of the
diffracted components
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Simulation Example Frustum Tracing

• Goals
• Find propagation paths around edges
• Render at interactive rates
• Allow dynamic sources, receivers, and geometry
• Method
• Frustum tracing with dynamic BVH acceleration
• Diffraction only in the shadow region
• Diffraction paths computed with UTD

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Step 1 Identify Edge Types (Preprocess)

• Mark possible diffracting edges
• Exterior edges
• Disconnected edges

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Step 2 Propagate Frusta

• Propagate frusta from source through scene

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Step 2 Propagate Frusta

• Propagate frusta from source through scene
• When diffracting edges are encountered, make
  diffraction frustum

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Step 3 Auralization

• If receiver is inside frustum
• Calculate path back to source
• Attenuate path with UTD coefficient and add to IR
• Convolve audio with IR
• Output final audio sample

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System Demo
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Future Work

• Direct comparison of UTD and BTM
• Numerical accuracy
• Computation time
• Subjective Tests
• Limited subjective tests of auralization with
  diffraction
• Static scenes
• Torres et al. JASA 01
• Calamia et al. Acustica 08
• Dynamic scenes
• None

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Additional Resources

• F. Antonacci, M. Foco, A. Sarti, and S. Tubaro,
  Fast modeling of acoustic reflections and
  diffraction in complex environments using
  visibility diagrams. In Proc. 12th European
  Signal Processing Conference (EUSIPCO 04), pp.
  1773 - 1776, 2004.
• P. Calamia, B. Markham, and U. P. Svensson,
  Diffraction culling for virtual-acoustic
  simulations, Acta Acustica united with Acustica,
  Special Issue on Virtual Acoustics, 94(6), pp.
  907 - 920, 2008.
• P. Calamia and U. P. Svensson, Fast time-domain
  edge-diffraction calculations for interactive
  acoustic simulations, EURASIP Journal on
  Advances in Signal Processing, Special Issue on
  Spatial Sound and Virtual Acoustics, Article ID
  63560, 2007.
• A. Chandak, C. Lauterbach, M. Taylor, Z. Ren, and
  D. Manocha, ADFrustum Adaptive frustum tracing
  for interactive sound propagation, IEEE Trans.
  on Visualization and Computer Graphics, 14, pp.
  1707 - 1722, 2008.
• R. Kouyoumjian and P. Pathak, A uniform
  geometrical theory of diffraction for an edge in
  a perfectly conducting surface. In Proc. IEEE,
  vol. 62, pp. 1448 - 1461, 1974.

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Additional Resources

• T. Lokki, U. P. Svensson, and L. Savioja, An
  efficient auralization of edge diffraction, In
  Proc. Aud. Engr. Soc. 21st Intl. Conf. on
  Architectural Acoustics and Sound Reinforcement,
  pp. 166 - 172, 2002.
• D. Schröder and A. Pohl, Real-time hybrid
  simulation method including edge diffraction, In
  Proc. EAA Symposium on Auralization, Otaniemi,
  2009.
• U. P. Svensson, R. I. Fred, and J. Vanderkooy,
  An analytic secondary-source model of edge
  diffraction impulse responses, J. Acoust.
  Soc. Am., 106(5), pp. 2331 - 2344, 1999.
• U. P. Svensson and P. Calamia, Edge-diffraction
  impulse responses near specular-zone and
  shadow-zone boundaries, Acta Acustica united
  with Acustica, 92(4), pp. 501 - 512, 2006.
• M. Taylor, A. Chandak, Z. Ren, C. Lauterbach, and
  D. Manocha, Fast edge-diffraction for sound
  propagation in complex virtual environments, In
  Proc. EAA Symposium on Auralization, Otaniemi,
  2009.

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Additional Resources

• R. Torres, U. P. Svensson, and M. Kleiner,
  Computation of edge diffraction for more
  accurate room acoustics auralization, J. Acoust.
  Soc. Am., 109(2), pp. 600 - 610, 2001.
• N. Tsingos, T. Funkhouser, A. Ngan, and I.
  Carlbom, Modeling acoustics in virtual
  environments using the Uniform Theory of
  Diffraction, In Proc. ACM Computer Graphics
  (SIGGRAPH 01), pp. 545 - 552, 2001.
• N. Tsingos, I. Carlbom, G. Elko, T. Funkhouser,
  and R. Kubli, Validation of acoustical
  simulations in the Bell Labs box, IEEE Computer
  Graphics and Applications, 22(4), pp. 28 - 37,
  2002.
• N. Tsingos and J.-D. Gascuel, Soundtracks for
  computer animation Sound rendering in dynamic
  environments with occlusions, In Proc. Graphics
  Interface97, Kelowna, BC, 1997.
• N. Tsingos and J.-D. Gascuel, Fast rendering of
  sound occlusion and diffraction effects for
  virtual acoustic environments, In Proc. 104th
  Aud. Engr. Soc. Conv., 1998. Preprint no. 4699.