Microstructure based effective stress formulation for partially ...
A comparison of partially specular radiosity and ray tracing for room acoustics modeling
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3PAA7 Beamer and Muehleisen 1 A comparison of partially specular radiosity and ray-tracing for room acoustics modeling C. Walter Beamer IV The University of Colorado [email protected] Research Supported by: The National Science Foundation Grant No. 0100196 Ralph T. Muehleisen Illinois Inst. of Technology [email protected]
Transcript of A comparison of partially specular radiosity and ray tracing for room acoustics modeling
3PAA7 Beamer and Muehleisen 1
A comparison of partially specular radiosity and ray-tracing for room
acoustics modeling
C. Walter Beamer IVThe University of Colorado
Research Supported by: The National Science Foundation Grant No. 0100196
Ralph T. MuehleisenIllinois Inst. of Technology
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Background• Diffuse Radiosity Theory presented at Spring
’02 meeting• Diffuse Radiosity Results Presented at Fall
’02 meeting• Early Partially Specular Theory presented at
Fall ’03 meeting
• The full Partially specular theory is too complicated to summarize and review for this presentation. See Beamer’s thesis or wait for our JASA papers to come out
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Super Basic Radiosity Theory• Break surfaces into patches• Compute steady state energy balance
between surfaces• Acoustic analog to
– Radiosity in Computer Graphics– Radiative Transfer in Thermodynamics– Luminous Radiative Transfer in Illumination
• Basically, we are solving an acoustic radiativetransfer equation (RTE)
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Partially Specular Radiosity• Basic (Diffuse) Radiosity assume all surfaces
are completely diffuse reflectors– Energy balance becomes a single matrix equation
• Partially Specular Radiosity assumes directional reflection– Can model specular or diffuse or anything in
between– Energy balance becomes a linear set of matrix
equations• Can be formulated as a 3-matrix equation• Luckily, these 3-matrices are sparse• Thank goodness for MATLAB
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Testing Partially Specular Radiosity• Three rooms were modeled
– Squash Court• Low diffusion at low freq, med diffusion at higher freq
– Small Office• Medium diffusion
– Empty Classroom• Medium diffusion
• Three simulations for each room– 90 % Specular reflection (CATT scattering = 0.1)– 50 % Specular reflection (CATT scattering = 0.5)– 100 % Diffuse reflection (CATT scattering =0.99)
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Computing Details• PS models utilized 20 to 125 surface areas
• Radiosity models were coded in MATLAB– PS Code was not easily vectorized and made
liberal use of structures which slows MATLAB– PS runtime increases with specularity
• 90% and 50% PS Runtimes were similar to CATT • 10x to 1000x speedup expected for a production code
– CATT runtimes increase with diffusivity• Diffuse model already runs faster than CATT
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The Squash Court
125 250 500 1000 20000.04 0.04 0.07 0.07 0.06
125 250 500 1000 20000.02 0.02 0.03 0.04 0.04
125 250 500 1000 2000
Ceiling/Walls - Painted Plastered Concrete
Octave Band [Hz]
Octave Band [Hz]
Floor - Varnished Hardwood
Walls - 2m high full width windowOctave Band [Hz]
Room Absorption Data
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Squash Court Prediction Comparison
• 90% PS prediction might be able to be improved with more boundary patches
• Fully diffuse predictions track very well but Diffuse Radiosity is MUCH faster to compute
Difference Between CATT and PS Predicted Lp in dB
Octave Band [Hz]
Model 125 250 500 1000 2000 4000
90% PS 0.9 1.2 1.0 0.5 0.6 1.050% PS 0.3 0.5 0.5 0.9 0.9 1.2Fully Diffuse 0.2 0.2 0.1 0.1 0.1 0.2
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The Empty Office
125 250 500 1000 2000 40000.02 0.03 0.03 0.03 0.03 0.02
125 250 500 1000 2000 40000.31 0.28 0.47 0.68 0.81 0.83
125 250 500 1000 2000 40000.14 0.06 0.04 0.03 0.03 0.03
Floor - Vinyl Tiles on ConcreteOctave Band [Hz]
Room Absorption Data
Walls - Painted PlasterboardOctave Band [Hz]
Octave Band [Hz]Ceiling - Mineral Fibre Acoustical Tiles
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Office Prediction ComparisonDifference Between CATT and PS Predicted Lp in dB
Octave Band [Hz]
Model 125 250 500 1000 2000 4000
90% PS 3.7 3.2 3.7 4.1 4.4 3.950% PS 2.3 2.0 2.4 2.7 2.8 2.8Fully Diffuse 0.1 0.1 0.1 0.1 0.3 0.3
• Much larger difference between PS and CATT than for Squash Court– Comparison to measured data (not shown here) shows PS
predictions are better and 50% PS model is best
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The Empty Classroom
125 250 500 1000 2000 40000.02 0.03 0.03 0.03 0.03 0.02
125 250 500 1000 2000 40000.31 0.28 0.47 0.6 0.71 0.83
125 250 500 1000 2000 4000
0.02 0.02 0.03 0.04 0.04 0.03
125 250 500 1000 2000 40000.15 0.11 0.1 0.07 0.06 0.07
125 250 500 1000 2000 40000.25 0.15 0.11 0.08 0.05 0.03
125 250 500 1000 2000 40000.03 0.04 0.11 0.17 0.24 0.35
Room Absorption Data
Ceiling - Acoustical tiles glued to concrete
Octave Band [Hz]
Octave Band [Hz]
Floor - Vinyl Tiles on Concrete
Walls - Painted Plastered ConcreteOctave Band [Hz]
Walls - Thin curtain over windowOctave Band [Hz]
Walls - Solid DoorsOctave Band [Hz]
Walls - BlackboardOctave Band [Hz]
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Classroom Prediction ComparisonDifference Between CATT and PS Predicted Lp in dB
Octave Band [Hz]
Model 125 250 500 1000 2000 4000
90% PS 2.9 3.0 2.9 2.8 2.6 2.450% PS 2.4 2.5 2.4 2.3 2.1 2.0Fully Diffuse 0.4 0.3 0.3 0.3 0.4 0.5
• Smaller difference between PS and CATT than for Empty Office– Again, a comparison to measured data (not shown here)
shows PS predictions are better and 50% PS model is best
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Conclusions• Partially Specular Radiosity method
compares well to tested ray tracing program– PS model is closer to measurements than ray
tracing• MATLAB Computation for PS is comparable
to commercial ray tracing but would be faster in commercial code
• For the typical rooms shown here, an assumption of 50% PS surfaces fits measurements better than 90% PS or fully diffuse.
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Questions?
