A Ray Tracing Algorithm Developed at Acoustical Engineering Departmentof the Federal University of Santa Maria (UFSM) in Brazil
Eric BRANDÃO(1) , Rodrigo DAL FIUME(1) , Gonçalo MORGADO(2) , William D’A. FONSECA(1) , Paulo MAREZE(1)(1) Federal University of Santa Maria, Acoustical Engineering, Santa Maria, RS, Brazil,{eric.brandao, rodrigo.dalﬁume, will.fonseca, paulo.mareze}@eac.ufsm.br(2) Godwit Labs, Brazil, goncalo@godwitlabs.com

Abstract
This paper presents a ray tracing algorithm developed as a research and teaching tool at the acoustical engineering course of the Federal University of Santa Maria in Brazil. The motivations to pursue this task and somenovel features of the code are presented. The results obtained so far were compared to some Odeon simulations.
Calculations on the Elmia Hall, extensively covered on the 2nd round robin of room acoustics inter-comparison
software, were also performed.

Keywords: room acoustics, geometrical acoustics, ray tracing, 2nd round robin, computer methods.

1

INTRODUCTION

Over the last decades, geometrical acoustics (GA) have been playing a major role in room acoustics design andauralization. Software packages that implement GA methods may have many different applications ranging fromarchitectural acoustics design [1] to real-time auralization [2–4].
If someone desires to use a software package for a project, for auralization or both, there is a need to calculate
the acoustic ﬁeld inside a room. Several methods and algorithms have been developed since the 1970s inorder to accomplish this task. Some of these methods are pure ray tracing [5], image-source [6] or radiosity
algorithms [7]. Furthermore, some of these software packages use hybrid methods, such as in Odeon [8].
A comprehensive review of geometrical acoustics algorithms is given by Savioja and Svensson [9].
In this paper, the development of a pure ray tracing algorithm is presented. It does not have the ambition ofcontributing to the current state-of-the-art in GA. Nevertheless, it should be seen as preliminary work on a more
ambitious and longer project. Another reason to consider only a pure ray tracing algorithm (in this step of the
project) is that the human resources involved in the assignment are limited. The code was developed as part ofindependent research (with no funding) by a professor of the undergraduate program in Acoustical Engineering(EAC) in Brazil. One may argue on behalf of using a commercial package to do research. Thus, on one hand,
our Acoustical Engineering course has a license of Odeon. On the other hand, annual licenses, support andupdates are expensive for the current Brazilian economic reality.
Therefore, in this work, the authors intent to validate and expose the results obtained with these in-house softwaretools running well-known algorithms. Moreover, it contributes to the creation of a platform that will allow thedevelopment of more sophisticated methods. Several features that improve the algorithm are also reported in
Section 2.2.

2

DESCRIPTION OF THE ALGORITHM

In this section, the work-ﬂow of the algorithm is described. Some novel features will be presented, as well asfunctionalities to be developed in the near future.

4638

2.1 Work-ﬂow
The algorithm presented within this paper works upon the basis of ray-tracing, similar to what is presented by
Kulowski [5] – with some new features. The input data consists of four struct variables: the geometry of theroom (vertexes coordinates and plane properties), the sound sources (sound power and coordinates), the receivers(coordinates) and algorithm controls.
The algorithm has the ability to deal with diffuse reﬂections. It occurs when the reﬂection is greater than aspeciﬁed transition order (TO). For those reﬂections, the ray comming out of a surface goes either on specular
or on a sorted direction. The probability of ray to go on a sorted direction depends on the scattering coefﬁcientof the plane hit by the section of the ray.
After all the rays are traced, the sound intensities are calculated to each source, receiver and ray according to
Eq. (1). These intensities are not assembled in ascending order. Then, for each source, receiver and frequency
band the reﬂectograms and decay curves are calculated. At this stage, intensities and time encounters are sorted
in time ascending order. Finally, the acoustical parameters such as T20 s, T30 s, EDT s, C80 dB, D50 %, Ts ms
and G dB are calculated from the equivalent reﬂectogram or decay curve. The average and standard deviation
over source-receiver pairs are also estimated for each parameter.
1W
I(t) =
2
Nrays π rrec

∏ Ri e−mt c0 ,(1)iin which t is the time encounter in s; c0 is the sound speed in m/s; m is the the frequency dependent air
absorption coefﬁcient in m−1 ; W is the sound power (in W) for a given frequency band; Nrays is the number
2 is the receiver radius at time instant t and e−mt c0 accounts for air absorption over distance.
of rays traced; rrec
The term ∏i Ri accounts for the the energy of the ray that is left in the room at ray-receiver encounter. It is the
cumulative product of the reﬂection coefﬁcients of all planes hit by a ray prior to the ray ﬁnding the receiver.
Ri = 1 − αi (for the direct sound ∏i Ri = 1.0).
2.2 Some interesting features
The algorithm was thought to have some features which make it different from the standard ray tracing algorithm[5]. It is necessary to acknowledge that tracing a large number of rays in a room is computationally expensive.
In this sense, there are two features that help save a lot of work.
The ﬁrst feature is that if a user decides to change the absorption coefﬁcient of any number of surfaces, it is notnecessary to run the ray tracing again. It is only required to calculate intensities, reﬂectograms and the acousticalparameters, which are not time-consuming steps.
The second feature is similar to what is described by Dalenbäck [10]. The receivers are allowed to grow in size
according to
2 c0 t .
r(t) = (2)
Nrays
Dalenbäck advocates in favor of this approach since a bigger receiver has a higher probability of being hit by
a ray. This point is exploited in Fig. 1, which shows two reﬂectograms1 and equivalent decay curves for alarge hall (see Sec. 3). Figure 1 (a) depicts the receiver that has 10 cm of radius, and it is forbidden to grow.
In Fig. 1 (b), it has an initial radius of 10 cm and grows up to 0.50 m, according to Eq. (2). It is easy to notethat the reﬂectogram in Fig. 1 (b) is more densely ﬁlled as time increases. Accordingly, the decay curve issmoother, allowing the correct calculation of acoustical parameters. If one increases the maximum receiver radius
to a reasonable values or use more rays these effects are even more dramatic.
Since as time goes by, the sound ﬁeld tends to be more diffuse in the room, the receiver growth is not expected
to play a downgrading role in the exactness of the calculation of reﬂectograms and in auralization [10]. In ourcase, the receiver is allowed to grow only after the transition order is reached. This increases the chances of
1 The simulations were performed considering 10000 rays.

4639

freq:2000 [Hz]; Source:1; Receiver:3

freq:2000 [Hz]; Source:1; Receiver:3
0

0

-10

-10

-20

Intensity [dB]

Intensity [dB]

-20

-30

-40

-30

-40

-50

-50

-60

-60

-70

-70

-80
0

0.5

1

1.5

2

2.5

Time [s](a) Receiver radius of 10 cm(constant)

3

-80
0

0.5

1

1.5

2

2.5

3

Time [s](b) Receiver radius of 10 cm(growing up to 0.5 m)(c) Monte Carlo simulation
for C80 dB

Figure 1. The inﬂuence of allowing the receiver to grow as the distance covered by the ray increases in its
travel through the room. The number of rays is 10000 and the initial radius of the receiver is 10 cm. In (c) aMonte-Carlo simulation for C80 .
ﬁnding exact specular pathways to be used in auralization (if a sufﬁcient number of rays are traced) . Additionally,
the receiver is allowed to grow to a certain maximum size, which can be speciﬁed by the user. This helps
keeping receiver sizes under control, specially if the number of rays traced are small. For instance, the receiverin Fig. 1 (b) grows from 0.1 m to 0.5 m. Also there is a check to prevent receiver sizes smaller than the initialreceiver size. This can happen after TO is reached and if one has a lot of rays and may cause undesired artifacts.
The third feature is the inclusion of Monte Carlo simulation for absorption coefﬁcient data. With this feature
an user can supply a percentile deviation expected in absorption data. The Monte Carlo simulation will run
and calculate a population of acoustical parameters, from which one can extract mean and conﬁdence interval
information. For instance, Fig. 1 (c) shows the mean value (red-solid/doted line), the conﬁdence interval for 95%
of values (red-shaded area) and the jnd (dashed-black line) for C80 . The simulation was performed assuming
a 20% variation in the absorption coefﬁcients of all materials. The point here is not to discuss uncertainty initself, but to present the feature. The motivation to write this feature comes from the paper by Vorländer [11].
At present there is a ﬁnal graduation work in progress covering this issue at our acoustical engineering course.
2.3 Future
Building this kind of tool is not an easy task and our team and resources are limited. Nevertheless, there area few features that we aim to pursue for the improvement of the tool. First of all, it is easy to recognize that
simple ray tracing schemes like this have several short-comings, such as low reﬂection density and the needof a large number of rays. In that regard it is intended to implement a framework that allows us to explore
other geometrical acoustics algorithms. There are also several other features that need some work like: source
directionality and receiver orientation (allowing the calculation of spatial parameters such as LF and LFC);
the calculation of parameters like U80 , STI and others and building an auralization module is also intended.
One of our aims is to make the tool available for free for research institutions. Although any of this seems
to be a novelty for the general community, it is our perception that it has allowed a great gain of knowledge
to the researchers. Similarly, it it the perception of the authors that having to deal with computer codes likethis is a good tool to improve students knowledge on the matter of room acoustics. Finally, and given theparallel workload involved in this type of problem we understand that the development of tools that make use ofheterogeneous computing platforms, nowadays cheap and quite common, will greatly improve the performance ofthe framework.

4640

3

RESULTS

Since 1995 there were several round robin initiatives displaying inter-comparisons between software packages
dedicated to room acoustics. The round robin I was published in 1995 [12] and explored the PTB auditorium
located in Germany, used mainly for speech. The round robin II was published in 2000 and explored the Elmia
Hall located in Sweden. The round robin III was published in 2005 and explored the PTB studio (with somedegree of variable acoustics) located in Germany. These three round robins included comprehensive measurementsof acoustical parameters such as T30 , EDT, C80 , D50 , Ts , G, LF, LFC and IACC. In the end of April of this year
(2019) the round robin IV was published [13]. This round robin includes signiﬁcant extensions of the previous
ones. A large database is provided including geometry ﬁles of several scenes to be tested (from basic scenes toinvestigate phenomena such as diffraction to 3 complex rooms). It also includes subjective analysis of auralization,measurements and calculations of several acoustical parameters.
The round robins are very important to software developers because they provide a chance to test implementation,
check for failures and drawbacks and improve the calculations. In this paper, a comparison of the code implemented with the results from round robin II is provided. On one hand, one can argue that this is a relatively oldround robin and more modern scenes and tests exists. This is a fact and also it is worth noting that the existing
software packages have improved their calculation algorithms and functionality over the last years. In part, this isdue to their participation in the previous round robins. So, on the other hand, participating in round robin II
allows us to take the small steps that would lead us to a better algorithm. Another point to be made is that thecomparison with other calculation algorithms is to some degree invalid, since these algorithms have improved
over the last years. Anyway, there is a comparison with experimental data, which is still very much valid. The
only speciﬁcs worth noting regarding the experiments is that, in round robin II, impulse responses were measured
with the use of MLS technique and nowadays exponential sweeps are a more common measurement strategy.
As pointed before, the Elmia Hall was explored in round robin II. This is a concert hall with a 1100 seats andwith a volume of 11000 m3 . There were 2 sound sources and 6 receiver positions calculated and measured inthis round robin. Since Odeon was one of the participants and our research group is an Odeon user, it seemed
intelligent to use the same geometry as Odeon did. It is worth noting that the results of Odeon calculations aremuch more accurate now that when Odeon participated in the round robin. The spreadsheet of round robin II isavailable at the PTB website [14].
A wire frame of Elmia Hall can be seen in Fig. 2. The ﬁgure also depicts one of the functionality of ouralgorithm – it is possible to see the direct sound (in blue) and reﬂections of 1st order for source 1 and receiver 4.
The reﬂectogram (beneath the wire frame) highlights the times of arrival and intensities at receiver 4.

Figure 2. A ray tracing showing ﬁrst reﬂection paths of order 1 at the Elmia Hall (S1R4).

4641

At present, the parameters our algorithm is able to calculate are: T30 2 , EDT, C80 , D50 , Ts and G. Figure 3 shows
the results for all source-receiver pairs at the 1000 Hz octave band. The experimental data is represented by thesolid black line. The results of our algorithm (named TREM) are displayed by the solid red line. Both black andred lines have a bigger thickness to make comparisons easier. The results of other calculation algorithms comein several colors and it is not possible to know who are each of the participants. It was decided to adapt theoriginal spreadsheet to include the data coming from TREM, while keeping the original data unaltered. Even the
Odeon results are the original ones, and as pointed before they have improved a lot in the last years. This will
be explored later.
For EDT the most disagreeing result is for source 2 and receiver 1 (S2R1), with a difference of roughly 0.5 s(20% and bigger than jnd). On the other hand, for most source-receiver pairs the difference between measured
and calculated T30 and EDT are well within the jnd range.
For the C80 and D50 some source-receiver pairs display a good result and for others (e.g. S1R1) the differences
are higher than the jnd of each parameter. This is an indication that either the reﬂection density and/or theexactness of the ﬁrst reﬂections are somewhat faulty in TREM. This can be attributed to the pure ray tracing
scheme used by TREM. An hybrid image source and ray tracing is expected to be more exact, as discussed
later with Fig. 4. The center time (Ts in ms) is another measure of energy balance of reﬂectograms (or impulse
responses). Figure 3 (e) displays the results of the round robin II and TREM. The results are in good agreementwith the experimental data, except for the pairs S1R1 and S2R2. On one hand, these source-receiver pairs did nothave good agreement for the C80 and D50 . On the other hand, the agreement with experimental data happened
for more source-receiver pairs to Ts than to C80 and D50 . For the strength factor (G in dB), TREM is also able
to calculate the parameter relatively well. The worst results were for the pairs S1R1 and S2R4, at the order of 2dB for these source-receiver pairs.
Overall, the acoustical parameters calculated by TREM display a good agreement with the experimental data
and were comparable to other package developers. It is reasonable to argument that, since round robin II dates
from 2000, it is to expect that the exactness of the other competitors have improved over the years. The fact that
TREM shows good results already is promising, tough. There is room for improvement, especially if commercial
packages raw data can be used as a reference for improvement in a similar way that the experimental data fromthe round robins can. This is what is exploited in Figure 4, which displays reﬂectograms and decay curves fora
modern Odeon calculation of the Elmia Hall and TREM.
In Fig. 4 (a) there is a refelctogram and decay curve for Odeon and in Fig. 4 (b) for TREM – both for source
1 and receiver 4. From Fig. 4 (a) and 4 (b) it is possible to notice the general structure of the reﬂectogram issimilar. The reﬂectogram from Odeon is much more densely populated by reﬂections up to a higher time. This
led to a more stable decay curve, in turn. The similarity of the general structure allows TREM to calculate theparameters with a good degree of exactness for most source-receiver pairs.
On the other hand, the details of calculated reﬂectograms are expected to be important for more precise calculations and auralizaation. In Fig. 4 (c) reﬂectograms and decay curves are compared for the ﬁrst 500 ms for source
2 and receiver 1 in Odeon and TREM. It is possible to see that, in Odeon [8], this part of the reﬂectogram is
more densely populated. This is attributed to the use of scattering of the energy of the image sources with theuse of early rays. So, there is energy being distributed over time instants not equal to specular paths between
source and receiver. For the same reason, the energies of the image sources are a little smaller in Odeon (part of
specular energy is scattered). In TREM, with a sufﬁcient number of rays, the time instants of early reﬂections are
somewhat well calculated and the intensities a litter over estimated. With this analysis it is tempting to conclude
that TREM is faulty only in the ﬁrst instants of the reﬂectogram. But in order to have a fact based certainty
more analysis have to be carried out, which will be done in the near future.
Figures 5 (a) and 5 (b) shows the relative mean errors for all acoustical parameters calculated so far for TREM
and all other participants. The error is calculated in Eq. (3).
2 T is also calculated, but it does not appear in round robin II.
20

4642

Round Robin II on RACS - ELMIA hall phase II

Round Robin II on RACS - ELMIA hall phase II

3,5

1
2

3,0

3

2,5

5

2,0

6

5DXF

3,5

1
2

3,0

3

2,5

5

2,0

6

5DXF

6DXF

1,5

8

6DXF

1,5

8

9DXF

1,0

13DXF

9DXF

1,0

13DXF

14DXF

0,5

15DXF

14DXF

0,5

15DXF

16DXF

16DXF

source - receiver pairsource - receiver pair(a) T30 in s(b) EDT in sRound Robin II on RACS - ELMIA hall phase II

S2R6

S2R5

S2R4

S2R3

S2R2

S2R1

S1R6

S1R5

S1R4

TREM

S1R3

0,0
S1R2

measured

S1R1

S2R6

S2R5

S2R4

S2R3

S2R2

S2R1

S1R6

S1R5

S1R4

S1R3

S1R2

S1R1

0,0

1
2

2,0

3
5

0,0

5DXF
6

70,0

1
2

60,0

3

50,0

5

40,0

6

5DXF

6DXF

-2,0

8

6DXF

30,0

8

9DXF

-4,0

13DXF

9DXF

20,0

13DXF

14DXF

-6,0

15DXF

14DXF

10,0

15DXF

16DXF

16DXF

source - receiver pairsource - receiver pair(c) C80 in dB(d) D50 in %Round Robin II on RACS - ELMIA hall phase II

S2R6

S2R5

S2R4

S2R3

S2R2

S2R1

S1R6

S1R5

S1R4

TREM

S1R3

0,0
S1R2

measured

S1R1

S2R6

S2R5

S2R4

S2R3

S2R2

S2R1

S1R6

S1R5

S1R4

S1R3

S1R2

S1R1

-8,0

1
2

14,0

5
5DXF

150,0

6

6DXF

2
3

10,0

5
5DXF

8,0

6

6DXF

6,0

8

100,0

9DXF
13DXF
14DXF

50,0

15DXF

8

4,0

9DXF
13DXF

2,0

14DXF
15DXF

0,0

16DXF

16DXF

source - receiver pairsource - receiver pair(e) Ts in ms(f) G in dB

S2R6

S2R5

S2R4

S2R3

S2R2

S2R1

S1R6

S1R5

S1R4

S1R3

TREM

-2,0
S1R2

measured

S1R1

S2R6

S2R5

S2R4

S2R3

S2R2

S2R1

S1R6

S1R5

0,0
S1R4

TREM

1

12,0

3

200,0

S1R3

measuredRound Robin II on RACS - ELMIA hall phase II

250,0

S1R2

TREM

Round Robin II on RACS - ELMIA hall phase II

4,0

S1R1

measuredmeasured
TREM

Figure 3. Room acoustics objective parameters for each source-receiver pair at the 1 kHz octave band.

4643

freq:1000 [Hz]; Source:1; Receiver:4

freq:1000 [Hz]; Source:1; Receiver:40

freq:1000 [Hz]; Source:2; Receiver:10

reflectogram (ODEON)
decay curve (ODEON)
reflectogram (TREM)
decay curve (ODEON)

0

-5
-10

-10

-20

-20

-10

-40

Intensity [dB]

Intensity [dB]

Intensity [dB]

-15
-30

-30

-40

-20

-25

-50

-50

-60

-60

-30

-70

-70

-35

-80
0

-80
0

0.5

1

1.5

2

2.5

3

0.5

1

1.5

2

2.5

3

-40
0

Time [s]Time [s](a) Odeon

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Time [s](b) TREM 1000000 rays(c) TREM 100000 rays

Figure 4. Reﬂectograms extracted from Odeon and TREM, for 1000000 rays and 100000 rays (source 1 andreceiver 4 at 1 kHz octave band).

ē =
1 N 
xc (n) − xm (n)  ,
∑
N n=1

(3)

where xc (n) and xm (n) are the calculated and measured values for a given source-receiver pair in a given
frequency band, respectively; and n spans through all source-receiver pairs and all frequency bands. The relative
mean errors are related to the jnd of each parameter. The advantages of using the relative mean errors is thatthey all ﬁt the same scaling and it can be easily estimated whether or not the error is in an audible range.

Round Robin II - Phase II
rel. mean error averaged over 12 positions and 6 octave bands

Round Robin II - Phase II
rel. mean error averaged over 12 positions and 6 octave bands
4,5

14,0

4,0

12,0

3,5
3,0

8,0
T30/s

6,0
EDT/s

4,0

rel. error

rel. error

10,0

2,5

D/%

2,0

C/dB

1,5
TS/ms

1,0

2,0
0,0

G/dB

0,5
1

2

3

5

5DXF

6

6DXF

8

9DXF

13DXF

14DXF

15DXF

16DXF

TREM

participant(a) Rel. mean error T30 and EDT

0,0

1

2

3

5

5DXF

6

6DXF

8

9DXF

13DXF

14DXF

15DXF

16DXF

TREM

participant(b) Rel. mean error D50 , C80 , Ts and G(c) EDT: Odeon vs. TREM

Figure 5. Relative mean error over all source-receiver pairs and over all frequency bands of the calculated room
acoustics objective parameters and a comparison between Odeon and TREM.
First of all, it is possible to see, in Fig. 5 (a) and 5 (b), that the relative mean errors obtained by TREM are in
the same range as the other participants. Although, all the relative mean errors of the participants seem to bebigger than 1.0 jnd, and thus, perceptible, this seems to be due to a poorer calculation in the lower frequency
bands. On one hand, this is a natural limit of GA methods, which do not take phase into account most of thetime. On the other hand, since the other participants should have improved their algorithm, the same task is left
to TREM in the near future. One of the things to be included is a frequency dependent scattering coefﬁcient,which is not the case in this paper.
Finally, it is suitable to compare TREM and a modern version of Odeon regarding some acoustical parameters.
Figure 5 (c) shows a comparison for EDT. The thick-solid curves shows the mean values for all source-receiver4644

pairs (blue for Odeon and red for TREM). The colored shaded regions shows the conﬁdence intervals (CI)
calculated for the inclusion of 95% of the data. It is possible to see that the mean values for EDT are in good
agreement for all frequency bands. In general, the mean value of the EDT is over estimated. The CI seems alittle shorter for TREM, which indicates a smaller variation along source-receiver pairs obtained by Odeon.

4

CONCLUSIONS

The algorithm reported in this paper seems to be working well at this stage. The results are promising, since thecomparison of the calculated parameters by TREM are in good agreement with the experimental data reported
in round robin II. This investigation also points to the need of some improvements of TREM and to the needof use of hybrid algorithms to further improve the results. The implementation was successful considering thelimited resources available. It will also allow the continuation of research and teaching of room acoustics atFederal University of Santa Maria (UFSM) in a non favorable economical scenario.

REFERENCES[1] Alban Bassuet, Dave Rife, and Luca Dellatorre. Computational and optimization design in geometricacoustics. Building Acoustics, 21(1):75–85, 2014.
[2] M. Vorländer and J.E. Summers. Auralization: Fundamentals of Acoustics, Modelling, Simulation, Algorithms,
and Acoustic Virtual Realityvorlander2008afa, volume 123. Springer-Verlag, 2008.
[3] Markus Noisternig, Brian FG Katz, Samuel Siltanen, and Lauri Savioja. Framework for real-time auralizationin architectural acoustics. Acta Acustica United with Acustica, 94(6):1000–1015, 2008.
[4] Dirk Schröder. Physically based real-time auralization of interactive virtual environments. PhD thesis, 2011.
[5] Andrzej Kulowski. Algorithmic representation of the ray tracing technique. Applied Acoustics, 18(6):449–469,
1985.
[6] Jeffrey Borish. Extension of the image model to arbitrary polyhedra. The Journal of the Acoustical Society ofAmerica, 75(6):1827–1836, 1984.
[7] Eva-Marie Nosal. Room sound ﬁeld prediction by acoustical radiosity. PhD thesis, University of British
Columbia, 2002.
[8] ODEON Room Acoustics Software User’s Manual Version 14, 2018.
[9] Lauri Savioja and U Peter Svensson. Overview of geometrical room acoustic modeling techniques. The
Journal of the Acoustical Society of America, 138(2):708–730, 2015.
[10] Bengt-Inge L Dalenbäck. Room acoustic prediction based on a uniﬁed treatment of diffuse and specular
reﬂection. The journal of the Acoustical Society of America, 100(2):899–909, 1996.
[11] Michael Vorländer. Computer simulations in room acoustics: Concepts and uncertainties. The Journal of the
Acoustical Society of America, 133(3):1203–1213, 2013.
[12] M. Vorlander. International round robin on room acoustical computer simulations. Proc. of ICA95, Trondheim,
Norway, pages 26–30, 1995.
[13] Fabian Brinkmann, Lukas Aspöck, David Ackermann, Steffen Lepa, Michael Vorländer, and Stefan Weinzierl.
A round robin on room acoustical simulation and auralization. The Journal of the Acoustical Society ofAmerica, 145(4):2746–2760, 2019.
[14] Ptb web site with data of round robins ii and iii, https://www.ptb.de/cms/ptb/fachabteilungen/abt1/fb-16/ag163/round-robin-in-room-acoustics.html, access in 01 of may 2019, 2019. URL https://www.ptb.de/
cms/ptb/fachabteilungen/abt1/fb-16/ag-163/round-robin-in-room-acoustics.html.

4645