Geometric Sound Propagation Anish Chandak & Dinesh Manocha UNC Chapel Hill

Sound Propagation Approaches   Numerical Methods   Solve Helmholtz Wave Equation   Accurate   Compute intensive (fourth power of frequency)   Not practical for interactive applications   Methods   Finite Element Methods [Otsuru,2004]   Boundary Element Methods [Ciskowski,1993]   Finite Difference Time Domain [Kunz,1993]   Digital Waveguide Mesh (DWM) [Savioja,1994]   Domain Decomposition [Raghuvanshi,2008]

Sound Propagation Approaches   Geometric Methods   Ray-Approximation of Wave Equation   High-frequency approximation   Fast   Highly dependent on the geometry details   Methods   Image Source [Borish,1984] [Dalenback,1992]   Ray Tracing [Krokstad,1968] [Kuttruff,1993]   Beam Tracing [Funkhouser,1998] [Funkhouser,1999]   Phonon Tracing [Kapralos,2004] [Bertram,2005]   Frustum Tracing [Lauterbach,2007] [Chandak,2008]   Acoustic Radiance Transfer [Siltanen,2007] [Siltanen,2009]

Geometric Sound Propagation   Shoot geometric primitives from sound source   The could cause: Direct Contributions Reflection Contributions Diffraction Contributions   Very high update rate for direct contributions   ~20-30 Hz update rate for higher order contributions

Image Source for Sound Propagation   [Berkley,1979] [Borish,1984] [Dalenback,1992]   Input: point sound source point listener scene geometry with acoustic properties   Output: pressure impulse response (IR)

Image Source for Sound Propagation   [Berkley,1979] [Borish,1984] [Dalenback,1992]   Advantages   Geometrically accurate simulation   No aliasing issues, especially for dynamic scenes   Hybrid approaches are popular   Disadvantages   Exponential blow up of virtual image sources   Too slow for dynamic and interactive applications   Handles only specular reflection

Image Source Method   Geometric sound propagation approach   Computes virtual image sources recursively from a sound source   Accurately find all the geometric paths from source to the listener   Impulse Response (IR) is constructed from the contributing paths   The impulse response is a pressure IR which is convolved with input dry signal

AN OVERVIEW Image Source Method

S S1 S2 S3 S4 S Image Source Method

S S1 S2 S3 S4 S L Image Source Method

S S1 S2 S3 S4 S L Image Source Method

S S1 S2 S3 S4 S L A Image Source Method

A S S1 S2 S3 S4 S L Image Source Method

S S1 S2 S3 S4 S Image Source Method

S S Image Source Method

S S S12 S13 S14 S15 Image Source Method

L S S S12 S13 S14 S15 Image Source Method

L S S S12 S13 S14 S15 Image Source Method

L S S S12 S13 S14 S15 Image Source Method

L S S S12 S13 S14 S15 Image Source Method

S S S12 S13 S14 S15 Image Source Method

 Two Step Algorithm 1. Computing image sources (From-point Visibility) 2. Validating paths from source to the listener Computing image sources Path Validation

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) convert energy IR into pressure IR for 3D audio rendering Note: audio signal is a function of pressure

Ray Tracing for Sound Propagation   [Krokstad,1968] [Kulowski,1984]   Advantages   Very Very Fast. Maps well to modern CPU and GPU architectures   Advanced field in Computer Graphics   Handles dynamic scenes efficiently   Handles diffuse reflection   Disadvantages   Sampling and aliasing issues   Aggressive acoustic simulation   3D Audio Rendering artifacts in dynamic scenarios   Cannot handle diffraction

AN OVERVIEW Ray Tracing Method

Step 1: Shoot Sound Rays Scene Geometry S Sound Source Listener L

Step 1: Shoot Sound Rays S L Shoot Rays From Source

Step 2: Trace Sound Rays S L

Step 3: Specular Reflections S L Based on Reflection Coefficient Annihilate Or Energy Based

Step 3: Diffuse Reflections S L Based on Scattering Coefficient Annihilate or Choose a random direction

Step 3: Construct Energy Histogram S L Collect Rays at the Listener

Step 3: Construct Energy Histogram S L Collect Rays at the Listener

Step 4: Pressure IR from Energy Histogram  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]

Beam Tracing for Sound Propagation   [Funkhouser,1998] [Funkhouser,1999]   Input: point sound source point listener scene geometry with acoustic properties   Output: pressure impulse response (IR)

Beam Tracing for Sound Propagation   [Funkhouser,1998] [Funkhouser,1999]   Advantages   Geometrically accurate simulation   No aliasing issues, especially for dynamic scenes   Has a pre-processing and interactive stages   Can handle moving listener   Handles diffraction   Disadvantages   Expensive pre-processing step   Cannot handle dynamic sound sources or geometry   Cannot handle diffuse reflection

AN OVERVIEW Beam Tracing Method

Beam Tracing for Sound Propagation Acoustic Geometry -- surface simplification Acoustic Material -- absorption coefficient -- scattering coefficient Source Modeling -- area source -- emitting characteristics -- sound signal Propagation Personalized HRTFs for 3D sound Late Reverberation Digital Signal Processing [Funkhouser,1998]

Example: Input Scene [Funkhouser,1998]

Step 1: Spatial Subdivision (preprocess)   Partition 3D space into convex regions (BSP Tree). [Wikipedia, Binary space partitioning]

Step 1: Spatial Subdivision (preprocess)   Partition 3D space into convex regions (BSP Tree).   Build adjacency graph. [Funkhouser,1998]

Step 1: Spatial Subdivision - Example [Funkhouser,1998]

Step 2: Beam Tracing (preprocess)   Compute Beam Tree   Node Information   Cell ID   Beam and its apex   Cell boundary   Parent node ID   Attenuation Need to cite the authors of these images.

Step 2: Beam Tracing - Example [Funkhouser,1998]

Step 2: Beam Tracing - Example [Funkhouser,1998]

Step 2: Beam Tracing - Example [Funkhouser,1998]

Step 2: Beam Tracing - Example [Funkhouser,1998]

Step 2: Beam Tracing - Example [Funkhouser,1998]

Step 2: Beam Tracing - Example [Funkhouser,1998]

Step 2: Beam Tracing - Example [Funkhouser,1998]

Step 3: Path Generation (interactive) [Funkhouser,1998]

Step 3: Path Generation (interactive)   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)

Step 3: Path Generation - Example [Funkhouser,1998]

Step 3: Path Generation - Example [Funkhouser,1998]

Step 3: Path Generation - Example [Funkhouser,1998]

Step 4: Auralization (Interactive)  Convolve IR with input sound signal  Use the directional paths to simulate 3D audio using HRTFs Impulse Response (IR) Sound Signal* = Output Audio *= Need to cite the authors of these images.

Frustum Tracing for Sound Propagation   [Lauterbach,2007] [Chandak,2008]   Input: point sound source point listener scene geometry with acoustic properties   Output: pressure impulse response (IR)

Frustum Tracing for Sound Propagation   [Lauterbach,2007] [Chandak,2008]   Advantages   Very Very Fast   Handles moving sources and listeners   Handles complex and dynamic geometry   Handles diffraction   Disadvantages   Could miss some important contributions   Cannot handle diffuse reflection

AN OVERVIEW Frustum Tracing Method

Frustum Tracing Overview Frustum Triangle Intersection

Frustum Tracing Results (7 cores) Theater 54 ∆s Factory 174 ∆s Game 14K ∆s Sibenik 71K ∆s City 72K ∆s SodaHa ll 1.5M ∆s diffraction NO YES #frusta56K40K206K198K80K108K time (msec)

AN OVERVIEW FastV: From-point Visibility Culling and Applications to Sound Rendering

FastV: An Overview

Results (Speed)

Results (Convergence)

Results (Convergence) Armadillo

Results (Sound Propagation)

Step 3: Auralization   If receiver is inside frustum  Calculate path back to source  Attenuate path and add to IR  Convolve audio with IR  Output final audio sample

Phonon Tracing   [Kapralos,2004] [Bertram,2005]   Inspired from Photon Tracing [Jensen,2001]   Input: point sound source point listener scene geometry with acoustic properties   Output: energy impulse response (IR)

Phonon Tracing   [Kapralos,2004] [Bertram,2005]   Advantages   Handles diffuse reflection efficiently   Disadvantages   Compute intensive   Cannot handle dynamic source and geometry

AN OVERVIEW Phonon Tracing Method

Phonon Emission Step [Deines,2008]

Phonon Emission Step [Deines,2008]