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COMPUTER MODELLING WITH CATT-ACOUSTIC Î
THEORY AND PRACTICE OF DIFFUSE REFLECTION AND
ARRAY MODELING
Adrian James, Adri an James Acoustics, UK (adrian@adrianjamesacoustics.co.uk)
Bengt-Inge Daenbck, CATT, Sweden (bid@catt.se)
Amber Naqvi, IoSR University of Surrey and Adrian James Acoustics, UK
(amber@adrianjamesacoustics.co.uk)
1. INTRODUCTION
This paper describes the room acoustics prediction and auraisation software CATT-Acoustic. It
concentrates on topics reevant to prediction quaity rather than on features such as use of coour
and simiar that instead wil be exempified during the presentation. Athough important for the user,
abundant features are of imited vaue if the underying prediction agorithms fail to predict wel in
many important cases. Specificay, the paper wil focus on the handing of frequency dependent
diffuse refection and oudspeaker array modeing. Frequency-dependent diffuse refection is
essential for the prediction of fundamental parameters such as the reverberation time (RT), whie
handing the sometimes very ong nearfieds are as essential for the prediction of sound from
arrays.
2. SOFTWARE BACKGROUND
To serve as a backdrop for the prediction method discussion beow, the software background is
briefy outined in this section.
The initial DOS-based software was written in 1989 and was used a combination of the image
source model (ISM) for eary refections and gobal ray-tracing for the ate decay. Aready in the
initial versions frequency-dependent diffuse refection was taken into account. In 1990 the first
auraisation impementation, using Lake DSP hardware, was finished [1]. During the years 1990-94
features were added but no major method changes took pace.
In 1995 a software convover was incuded so that the compete auraisation process coud be
performed on a standard PC, athough the cose reationship with Lake DSP continued with head-
tracked auraisation [2] and Ambisonic repay options. Essentiay the same method was used up to
and incuding the first 16-bit Windows version in 1996 (v.6.0), and was successful in the first
international round-robin on room acoustics prediction [3] where CATT was one of ony three
programs that were judged to give reiabe and useful resuts. Of these three, 5 of the 8 predicted
measures were best evauated by CATT-Acoustic. With v.6 aso cassical ray-tracing [4] was added
for audience area coour mapping. However, during 1990-95, B-I Daenbck aso worked haf-time
in the Chalmers Room Acoustics Group [5] deveoping a more advanced prediction and auraisation
method resuting in a Ph.D. thesis [6].
In 1998, v.7 for 32-bit Windows was reeased introducing Randomised Tai-corrected Cone-tracing
(RTC), a simper but more robust variant of the research method. The RTC, detaied beow, is a
very general method useful for prediction of acoustic parameters as wel as for auraisation, and
remains the main prediction method in CATT-Acoustic. Aso reeased in 1998 was a fundamental
functionaity reated to array modeing: the DLL Directivity Interface (DDI) that enabed run-time
array-modeing incuding handing of the nearfied and DSP-settings for beam-steering.
Computer Modeing with CATT-Acoustic Î A James, B-I Daenbck , A Naqvi
3. DIFFUSE REFLECTION
Before the prediction methods empoyed are described a question has to be answered. Why is
diffuse refection so important in room acoustics prediction? For the answer it is useful to
characterise rooms according to:
  their mixing properties : i.e. basicay to what degree the room shape and surface
orientations are such that rays risk being ocked into particuar directions (e.g. between
parael was).
  their absorption distribution : i.e. if al surfaces have simiar coefficients, or if some
surfaces are hard whie other are very absorbent.
First we have the simpe cases: rooms where the shape acts as mixing and where the absorption
distribution is even. Here cassical Sabine theory works very wel and prediction using specuar-
ony methods can be quite successfu. Then we have the other extreme: rooms that are non-mixing
and with uneven absorption distribution. In these rooms Sabine wil dramaticay under-estimate the
actual RT whie specuar-ony methods wil dramaticay over-estimate the RT. To iustrate this a
case from consutant practice is used, see Figure 1.
Figure 1 Sports hal 43 x 23 x 7 m
3
. The ceiing is mosty covered with high-absorbing materia,
remaining surfaces are hard. T
Sabine
@ 1 kHz was 1.9 s whie the actuay measured T
30
was 5.7 s.
The acoustic consutant invoved [7] recommended pacing high-absorbing material between every
second beam pair in the ceiing (ca. 50% coverage giving an effective ceiing absorption coefficient
of 0.43 @ 1 kHz) and additional high absorption on at east one end wal and one side wa.
However, to save money the contractor instead chose to use ony the ceiing absorption and to
eave the rest basicay as concrete. With ony the ceiing used for absorption T
Sabine
@ 1 kHz was
1.9 s but when the RT was actuay measured it was 5.7 sec. This is a cear case of a non-mixing
shape where handing of diffuse refection is absoutey necessary. Tabe 1 ists the RT predictions
at 1 kHz using various methods and room modes.
Computer Modeing with CATT-Acoustic Î A James, B-I Daenbck , A Naqvi
Method/model
Scattering coefficient
(s @ 1 kHz)
RT @ 1 kHz (T
30
)
Sabine, detaied model
1
N/A
1.9 s
Sabine, simpe model
2
N/A
2.1 s
Measured
N/A
5.7 s
Detaied model
1
s
beams
= 0.22
3
, s
rest
= 0.08 5.1 s (10% error)
Simpe model
2
s
ceiing
= 0.80, s
rest
= 0.08 5.9 s (3% error)
Detaied model
1
specuar-ony, s = 0 13.0 s
Simpe model
2
specuar-ony, s = 0 12.0 s
Table 1 Predicted and measured RTs forthe sports hall.
1
with beams as in Fig.1,
2
flatceiling with high
diffusion,
3
auto edge diffusion (see below).
An interesting note here is that the sports hal project (ca.1995) was initiay cacuated with CATT-
Acoustic v.6 as wel as the consutants own in-house ray-tracing software, which aso handed
diffuse refection. The resuts were very simiar to those in Tabe 1, which were modeed in CATT
v.7.2. However, the frequency dependence of diffuse refection has not yet been addressed since
the exampe above ony hods for 1 kHz. Generay the frequency dependence has to be incuded
for purey physical reasons, and Figure 2 schematicay iustrates why. For a more general
discussion about diffuse refection in computerised prediction, see [8].
a)
b)
c)
l
l
l
D
D
D
Figure 2 Schematic description ofhow the ratio between surface roughness (D) and wavelength (l)
determines the diffusion.a) l << D :geometricalmixing (effectively acts as diffusion),b) l = D :high
diffusion,complex actualbehavior,c) l >> D :low diffusion.
4. PREDICTION METHODS
With the exampe in the previous section in mind, we can now ook at the two main prediction
methods empoyed by CATT-Acoustic ; ray-tracing and randomised tai-corrected cone-tracing.
RAY-TRACING FOR AUDIENCE AREA MAPPING
Audience area mapping is based on cassical ray-tracing with fixed-sized spherical receivers paced
in a grid over defined audience areas. Frequency-dependent diffuse refection using the Lambert
distribution [4] is taken into account by randomising the directions of those rays which are
determined to refect diffusey off a surface (as dependent on the scattering coefficient). An
Computer Modeing with CATT-Acoustic Î A James, B-I Daenbck , A Naqvi
exception is that direct sound is handed deterministicay without rays. When frequency-dependent
diffuse refection is taken into account (and ony when it is taken into account) ray-tracing is a very
robust prediction method. However, the echogram from ray-tracing is difficut to use for auraisation
since, unike with the RTC, the refection density growth over time is unnatura. Hence, ray-tracing
is ony used for mapping of measures such as C
80
but not for auraisation or a detaied echogram.
However, room acoustical measures predicted in CATT using frequency-dependent diffuse ray-
tracing are virtuay identical to those predicted by the more eaborate RTC.
RANDOMISED TAIL-CORRECTED CONE-TRACING FOR DETAIL AND
AURALISATION
The unique RTC is a combination of three different methods, compensating and correcting for
weaknesses in each of these three methods. The program uses scattering coefficients which are
normay estimated based on general guideines and input by the user in the same way as
absorption coefficients, but an automatic edge diffusion can aso be used. For hard smooth objects
ike tabes and refectors, a size- and frequency- dependent scattering coefficient is optionay
cacuated automaticay
1) Image Source Model (ISM) for 1
st
and 2
nd
order specuar refection so that the most important
eary refections are aways incuded independent of how many rays are used. A weakness of
the ISM is its inefficiency for high-order refections, but up to 2
nd
order it is aways fast.
2) Direct diffuse radiation for 1
st
order diffuse refection. Many smal diffusey radiating surface
sources are distributed over each diffusing surface. From the actual sound source, vectors are
drawn to each diffuse surface source and from each of those to the receivers (taking occusion
into account). To give the highest geometrical accuracy where it is needed, the number of
these surface sources is increased for surfaces with ow absorption coefficients and high
scattering coefficients.
3) Randomised cone-tracing for higher order refections where ray directions are randomised ike
in ray-tracing so that, unike with specuar cone-tracing, diffuse refection can be taken into
account.
A weakness of ray-tracing is that the receiver sphere must be fairy arge and the eary part detail
therefore suffers. The use of cone-tracing and the ISM compensates for this ack of detai. Cone-
tracing aso gives a refection density which grows with t
2
(t=time) which makes the resuting
echograms we-suited for natura-sounding auraisation. On the other hand, a weakness of cone-
tracing is a ray-density dependent ate refection oss and that is corrected for by an automatic
refection growth extrapoation [6]. However, the more rays/cones that are used the ess the
extrapoation needed.
5. ARRAY MODELLING INCLUDING THE NEARFIELD
The methods described above perform very wel for estimation of refected sound and thus the ful
echogram. However, with non-simpe sound sources the directivity aso needs to be handed in
sufficient detai. Manufacturers and researchers are now measuring ful space directivity at ever-
increasing resoutions, going from 10» and 1/1-octaves to 5» and 1/3-octaves. In some cases even
higher resoutions incuding phase is discussed.
However, with this focus on higher resoutions a fundamental property of oudspeaker arrays
appears to have been forgotten even in dedicated sound system software: the extended nearfied.
The now very popuar ine arrays (e.g. Duran Audio Inteivox and Target systems, L-Acoustics
V-DOSC/dV-DOSC, JBL VERTEC and several other under deveopment) are essentiay cyindrical
Computer Modeing with CATT-Acoustic Î A James, B-I Daenbck , A Naqvi
1/r-radiators up to very arge vaues of r (often > 100 m). Many commercial sound-system
modeing programs stil treat these as spherical 1/r
2
-radiators. In other words, these programs take
the farfied directivity of the array and appy it in the nearfied. This method may work for singe
speakers but can give widy incorrect resuts for arrays such as coumn oudspeakers or arge
central custers. To remedy this, in 1998 CATT deveoped a "DLL Directivity Interface" (DDI) that
did not just create an equivaent far-fied baoon from coherent summation of the array eements but
where the summation was done ÐiveÑ during run-time at each distance, azimuth and eevation
required, thus aso handing the nearfied.
Since a DLL is an actual program it can aso hande beam-steering. The first commercial ine array
that used the DDI was the Duran Audio Inteivox where DSP-settings for
AZIMUTH
,
FOCUSDISTANCE
and
OPENINGANGLE
simpy can be seected in the CATT DLL interface, in much the same way as
they are seected on site when the oudspeaker is programmed. Even if farfied-ony modeing of
such an array worked, it woud be extremey cumbersome to create an equivaent baoon for al
possibe DSP settings since each of the three parameters can be seected in very fine increments
(0.1 unit steps). Figure 3 shows a comparison of predicted poar diagrams at different distances for
an Inteivox 2c. Note that not ony the on-axis evel (as compared to 1/r
2
) changes with distance but
aso the shape of the baoon. Figure 4 shows a vaidation of the modeing as compared to an
outdoor measurement.
axis
3 m
7 m
10 m
20 m
Figure 3 Duran Audio Intellivox 2c,27 m long DSP-controlled column array.DSP settings:
AZIMUTH
= -1»,
FOCUSDISTANCE
= 40 m,
OPENINGANGLE
= 6».Polars are plotted at2»resolution,10 dB/div.
120
Measured
115
Simulated (DuranAudio)
110
Simulated (CATTDDI)
105
100
dB
spl
95
90
85
80
1/r
2
¼ -6 dB/distance-
doubling
> 10 dB difference
75
70
1
10
100
distance (m)
Figure 4 Validation ofDuran Audio Intellivox 2c DDIprediction at1 kHz,free-field on-axis.
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