PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Advances in diffusive surface design using 3D architecturalparametric modelling programs
Louena SHTREPIPolitecnico di Torino, Italy

ABSTRACT
Diffusive surfaces need to be optimally designed for both acoustic performance and aesthetic values. These
aspects are at the heart of the design workflow and should respond to the requirements of both architects andacousticians. Advances in parametric modelling through digital tools have led to the integration of
performance investigations and architectural design process. Moreover, parametric modeling software arealso useful tools for manufacturing. Indeed, they can reduce the production time as they can easily be
integrated inside the manufacturing process.
Although, it is more than a decade that the standard ISO 17497:2004 has proposed the scatteringand diffusion coefficients measurements, further work is needed in order to increase designers’
awareness on diffusive surface design through simple design rules and approaches.
This research goes through three steps. First, it investigates the diffusive surface properties
databases in order to extrapolate basic geometric guidelines for diffusive surface optimization. Second,
it analyses a series of case-studies that apply the parametric modeling to the design of diffusive
surfaces. Finally, it suggests a design process for diffusive surfaces by integrating parametric models
and acoustic simulation aiming to provide architects and designers with rapid visual and acoustic
feedback at a preliminary stage of their design.
Keywords: Sound, Simulation, Diffusers, Scattering, Parametric modelling

1. INTRODUCTION
Diffusive surfaces are essential elements that determine the acoustic quality in performance spaces
in terms of first-order reflections control (1, 2). They are used also in other environments, such asclassrooms or outdoor spaces, to increase speech intelligibility (3) and reduce sound noise levels (4,5). Diffusers have continuously challenged acousticians’ abilities in performance and proper use
within different environments; they have also tackled the creativity of designers, as these surfaces
strongly determine the visual outcome of the space (6). Only a few documented cases benefited froman integrated approach of both these two aspects (7-10). A parametric design thinking (PDT) (11)results appropriate and necessary to deal with the complexity of these surfaces. This approach allows
for a greater level of detail and differentiation for the entire space as well as for each single building
component. Therefore, further research is needed to highlight the benefits of PDT application to thecomplexity of the design of diffusive surfaces, in order to obtain a richer design and meet the acoustic
performance requirements. As it is reported in Wortmann and Tunçer (12), the strength of PDT does
not lie in generating many design variants, but rather in realizing highly specific, differentiated, rulebased designs. The design process has increased its scale increasing the number of professionals that
include architects, consultants and contractors. Therefore, it is required to practice PDT for a more
efficient design process, which highlights the need for software and programming language that allow
for data exchange. Based on this approach, this work aims to highlight the new perspectives of the
diffusive surface design that integrate computational and materialization tools.
Acoustic performance requirements are related to the scattering coefficient and the diffusion
coefficient (13), introduced in the standard family ISO 17497 (14, 15) which has eased theconstruction of reliable database of scattering and diffusion coefficients (6). These data are not only
necessary to compare different diffusers but are also adoptable as input data for acoustic simulationsin the preliminary conceptual or verification phase of the project (16-18). However, thesemeasurements are usually costly and time-consuming; therefore, they are mostly limited to researchand high budget design projects.
To overcome such limits, accurate prediction models have been validated (19-21), enabling to2289

optimize diffusers and control their properties at different incident angles (22). The most common
example of optimization concerns the Schroeder diffusors. Cox (23) showed the optimization process
through iterative boundary element method (BEM) based simulations. Other works showed theapplication of Finite Elements Methods (FEM) and Finite Difference Time Domain (FDTD) for multiobjective optimization starting from the design of the sonic crystal sound diffuser (SC D) effective at
low frequencies (24) and sound phase diffusers (25). Orlowski (26) and Cox (27) showed cases ofcurved diffusors optimization, and profiles of optimum diffusers were suggested in Takahashi (28).
However, the high computational cost of these methods makes them unadoptable in the early design
stages, when a high number of solutions are rapidly produced and discarded. Therefore, rapidity is
chosen over accuracy allowing the assessment of non-standardized solutions, which require an
exchange of information also with the fabrication process aspects. Acoustic performance as a key
design factor of the built environment has been pointed out in recent studies (29). Reinhardt et al. (8)investigated the design affordances of acoustically efficient patterns for sound scattering throughcomputational design and robotic fabrication. Peters and Olesen (7) used rapid prototyping for aneasier fabrication of scattering surfaces samples based on hexagonal elements with varied depth andwidth. The data obtained by measurements according to ISO 17497-1 method were used to inform theparametric design tools for the performance optimization. Further, visionary explorations suggest to
deploy robots to evaluate the designs of diffusive surfaces and directly react on the measured results
during the fabrication process within a given design framework, i.e. a process of architectural andacoustic tuning (29).
All the presented case studies imply a workflow that includes development of computational design
tools, geometry generation, fabrication of test surfaces, measurement of acoustic performance, andthe integration of these data into a generative tool (7-10). This approach is subject to continuous
evolution and requires a customization of existing software through computer-programming (12). As
highlighted by Whitehead (30) most designers already think programmatically, but since they arelacking the time and the inclination to learn programming skills, they cannot express or explore thesepatterns of thought. Therefore, a new professional figure might be needed to embrace design andacoustic knowledge in order to generate valid solutions from both aesthetical and acoustic point ofview with smaller effort.
This work aims to give simple geometrical guidelines for the optimization of diffusers performancebased on a literature review. Second, it analyses four case-studies that apply PDT to diffusive surfaces
design, in order to identify the workflows of the optimization process. Finally, it suggests a design
process for diffusive surfaces by integrating parametric models and acoustic simulation aiming toprovide architects and designers with rapid visual and acoustic feedback at a preliminary design stage.

2. DIFFUSERS OPTIMIZATION
The acoustical characterization of diffusive surfaces relies on two standards: ISO 17497-1:2004(14) defines the measurement of the random-incidence scattering coefficient in diffuse field as theratio of the non-specularly reflected sound energy to the total reflected energy; ISO 17497-2:2012(15) defines the measurement of the directional diffusion coefficient in free -field as a measure ofdiffusers quality. Both these coefficients are frequency dependent single numbers and all the dataobtained from these measurements makes easier the comparison between different surface treatments(13). Diffusers performance optimization aims to maximize both these parameters; to achieve thisgoal, know-how on the acoustic effects of a large number of geometrical variables is necessary. Thisknowledge can be based both on a systematic analysis of the literature and an ad hoc optimization
when a fabrication system and a measurement set-up can be easily integrated. Furthermore, acomputational process can be integrated in the design process to exploit the potential of parametricmodelling of different topologies and deduce design rules.
2.1 Diffusion coefficient optimization
A good diffuser has the ability to uniformly scatter in all directions, rather than just move energy
away from the specular angles (22). To this aim, curved diffusive surfaces can easily achieve higher
uniformity of the polar distribution of the scattered energy. As shown in Cox and D’Antonio (6),geometrical elements organized in arrays and modulated, for example, as Schroeder diffusers arelikely to generate a good spatial distribution. Therefore, an asymmetrical base shape as well as the
reduction of periodicity are preferred.

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Two important studies (31, 32) have presented deep-subwavelength diffusing surfaces based on
acoustic metamaterials, namely metadiffusers. They have redesigned the Schroeder diffusers based on
the concept of an acoustic metasurface in order to obtain surfaces with broadband uniform spatiallydependent reflection coefficients optimization. This methodology has led to ultrathin diffusers named
broadband metadiffuser only 3 cm thick, while conventional solutions are 69 cm thick, effective at
250Hz. However, they are still at an embryonic stage from the real-world application perspective.
Table 1 – Summary of the design rules for diffusive acoustic surfaces basedon the design at the level of the single scattering elements
Pattern

Design rule

Effectiveness on scattering anddiffusion

Ref.

Pyramids
Extruded profiles(Schroeder diffusers)
3D diffusers
Rib structures

Increased height
Increased height

Increase at Low and Mid frequencies
Increase at Low and Mid frequencies

(33)
(34)

Height > 20 cm
Height > 18 cm and width of 10 cm
Use of different heights in the same
panel

(35)
(36)

Periodic type diffusers
based on rib structures
Fractal order

Square section (5cm, 10cm and
22cm)
Use
of
different
sizes
simultaneously
Randomization

Increase at 500-3150Hz.
Increase at < 500Hz
Increase at 125-4000 Hz (smoothercurve of the frequency dependent
scattering)
Increase at Low and Mid frequencies
Broadband; Higher uniformity in thepolar distribution
Increase at 500-1000Hz and at highfrequencies, starting from 3.15 kHz(37)

Profile shape

Distance

Coveragedensity

Configuration

Size

VariableRandom array of cubes(20cm)(3)

Penrose configuration.

Aperiodic

Increase at 500-1000Hz

(36,
38,
39)
(37)

Cubes of 20cm

Coverage density around 50%.

Broadband(36)

Hemispheres
1D, 2D and 3D diffusers
Structures of 2.5 cm

Coverage density around 57 - 58 %
38%, 46% and 57%, respectively.
20 cm and 40 cm

Broadband
Broadband
Increase at 500-2000Hz

(38)
(35)
(37)

Periodic rectangular ribs of
4.7 cmperiodical profiles

15.1 cm and 30.2cm

(21)

Wave
Extruded triangles

Sine sweep profile
Triangular profile

Alternation of concave andconvex surfaces
Prismatic elements

Oriented orthogonal to each other

Decrease of the scattering values in
the frequency range 500-3150Hz
High frequencies are improved bytriangular and semicircular shapes;
mid frequencies benefit by therectangular profile
Increase High frequencies
only for specific generator angles.
(30°<χ<45°)
Broadband(37)

Deep triangular prisms

Asymmetric profile

Lead to higher scattering values
compared to pyramids or plates of thesame dimensions
Broadband

Rectangular, triangular andsemicircular profiles

Prismatic elements

(40)

(41)
(6)
(42)

(43)

2.2 Scattering coefficient optimization
Table 1 shows a summary of the design rules that can be deduced form the current available
literature. This data can be useful at the conceptual phase of the design workflow.
The size of the scattering elements is the first design aspect that can be controlled. The analyticalmodel in (13), that is f=c/2a or f=c/2h, shows a linear relation between the frequency and the size
(a=width or length, and h=height) of the scattering elements and provides the frequency at which
scattering becomes effective; for smaller frequencies only the specular mode is reflected by the profile.
However, according to ISO 17497-1 (14), the height of the diffusive elements is restricted to a2291

maximum of 1/16 of the diameter of the measurement rotating table (≈24cm).

3. EVALUATION OF THE DIFFUSIVE SURFACES
The above summary shows that the actual know-how on geometrical parameters impacting on
acoustical performance relies on a great number of measurements. The retrieved database could be
used to test the accuracy and the reliability of prediction models to further improve the entire
workflow of a design process.
3.1 Prediction of Sound Scattering and Diffusion
Different theoretical models based on FEM and BEM methods have been used to analyze the soundwaves reflected by a diffusive surface (19). Usually, these methods require advanced theoreticalknowledge and very long calculation times which prevent an immediate feedback. These drawbacks
leave designers apart from the acoustical performative investigation of the surfaces they design.
Acoustic performance of single surfaces can be integrated into architectural design workflows (710) by adopting parametric modeling and computer programming techniques. The most preferredenvironments are usually visual programming environments, such as Grasshopper: it allows the users
to drag-and-drop predefined operations and connect them into a directed, acyclic graph (44). Acoustic
analysis within Grasshopper can be made through the plug in Pachyderm Acoustics (45): this software
package integration allows for the development and investigation of performance driven geometries
at a higher complexity level. A process rationalization leads to a series of mutually informed
computational clusters and enables a completely digital workflow from the concept phase to
manufacturing (46).
3.2 Fabrication
The prototyping phase as well as the final output of a design workflow are strongly influenced bymaterialization concepts (47). As shown in Gursoy and Ozkar (48), computational formalisms aim toinclude material aspects of design additional to the visual ones. This approach can be applied also to
the integration of the acoustical performance.
The versatility and adaptability of different fabrication techniques such as 3D printers, CNC
milling machines, and industrial robots have enabled the exploration of new building techniques aswell as the generation of very complex surfaces (7-10). Also the fabrication aspects are subject tocontinuous research since there are still limitations regarding the samples size in 3D printed samples
and the optimization of tool paths in CNC manufacturing. The adoption of robots enables the
exploration of complex topologies with higher precision, even for scaled surfaces (47). The design
rules should consider these limitations very carefully since it determines the product costs.

4. CASE STUDIESThe approaches introduced below propose the development and testing of a large number ofalternatives integrating the acoustic performance of diffusive surfaces as one of the design criteria.
These approaches allow to shift from a validation procedure done at the end of the design process
to a conceptual design tool that allows acoustics performance to become part of the conceptualarchitectural design strategy (7).
4.1 Case study 1: Hexagonal structures
The design workflow proposed by Peters and Olesen (7), shows how the possibility to test andmeasure a large number of cases would allow the computational tools to learn and have higher
predictability power for future design. Machine learning techniques could help to explore extreme
design solutions to overcome the current measurement limitations. This workflow relies on thefollowing steps (Figure 1):(i) Three different topologies have been generated in a first conceptual phase and architecturaldesign parameters are specified. (ii) A hexagonal diffusing structures is chosen for the further steps
using the digital tools (a Microstation Visual Basic) and is parametrically designed based on simple
rules related to well depth and well width. (iii) Six options at 1:10 scale are fabricated by using a
2Corps 3D printer and generating circular samples useful for the next step. (iv) The scattering
coefficient for all these surfaces is measured in agreement with the ISO 17497-1. This is the mostchallenging step, since it is affected by a large number of uncertainty factors. However, it allows to2292

obtain the acoustic effect of the topological parameters, that is, of well depth on the frequency
distribution of scattering values and well width on its magnitude. These are considered as the acoustic
design aims. (v) The collected data are used as input for the design tools and allow to explore further
alternatives without necessarily performing the measurement phase.

Figure 1 – Case study 1 workflow: design rules, digital tool, fabrication and measurements details.
4.2 Case study 2: Micro-Design structures
Here the conceptual framework and pattern language available for acoustic scattering are extended
by highly flexible robotic fabrication in a search for “acoustic effects of complex architecturalgeometries” (8). The iterative design process consists of the following steps (Figure 2):(i) First, architectural design parameters are set, along with the acoustic design aims (e.g. scattering
coefficient spectrum). Parametric hexagonal and curvilinear splines are used to obtain two different
design alternatives through the parametric digital tool GH Grasshopper (a plug-in of McNeel Rhino
visual scripting environment). Design parameters for hexagonal splines are surface angles, height,
depth and directionality of the elements; in curvilinear splines, a variable number (up to 9) of attractor
points are used to orient and control the depth of the created isocurves. (ii) The computational designof specific surface micro-geometries is performed. The toolpath of the robot is adjusted in KUKA|prc,
which is a Rhino McNeel plug-in for fabrication. (iii) A CNC milling and a 7-axis robotic fabricationof physical scale model test samples is made in the form of circular samples useful for the next step.
The samples are designed with 310 mm diameter and 19 mm depth and prototyped in subtractive
cutting processes in XPS Styrofoam and wood. (iv) Acoustic measurements in a 1:10 scaled
reverberation room and analysis of sample performance are implemented based on ISO 17497-1. (v)Finally, design refinement is made, and further iterations are performed if necessary. At this point theangle of the sound reflection is linked to the robotic toolpath, thereby controlling the depth of thesample structure in order to obtain the desired reflection through the reverse process.

Figure 2 – Case study 2 workflow: design rules, digital tool, fabrication and measurements details.
4.3 Case study 3: Milled wood panels - students workshop
New simulation methods made possible for architects to calculate and digitally visualize acoustic
properties and how geometric variations affect its performance (9). The entire workflow is first
digitally tested; only the final, optimized result is fabricated. This is as an attempt to establish a design
method that incorporates simulation of acoustic performance and robotic fabrication of milled wood
panels, based on the following steps (Figure 3):(i) Design geometric specifications are left open to each student in order to explore the limits ofthe design process on creativity and cognitive process. (ii) This case study groups into a computational
design system four clusters related to (a) the Path Generation, where the user directly manipulates thecurve-based milling paths and informs the next cluster; b) Geometry Generation cluster, where the2293

user performs a subtractive process of removing material and graphically visualizes the resulting
milling simulation. The geometries are generated using parametric modelling based on Rhino andGrasshoper tools; c) the geometric shape is tested in the Acoustic Analyses cluster through simulations
with Pachyderm Acoustics and the performance is compared to the chosen target (e.g. high scattering
coefficient). This step informs the first cluster creating new milling paths and after the second cluster
step it also generates new optimized shapes; d) the last cluster is named Robotic Simulation and uses
the KUKAprc package to simulate the fabrication process. An optimization of the fabrication process
can be performed at this step and inform the first cluster. The simulations hold the potential of acting
as valuable feedback for the next iteration of re-designed and increasingly informed curve geometry.
(iii) The optimized solutions are fabricated through a KUKA KR300R2500 with a 7.5KW CNC spindle
mounted as its end effector.
The authors have highlighted some of the of the digital tools limitations that made impossible acontinuous data flow between the four clusters. However, they noted that an immediate visualfeedback was extremely helpful at the different levels of the workflow.

Figure 3 – Case study 3 workflow: design rules, digital tool, and fabrication details.

Figure 4 – Case study 4 workflow: design rules, digital tool, fabrication and measurements details.
4.4 Case study 4: Voronoi structureThis case study aimed to implement a feasible method with a rapid visual feedback that could help
the designer at the conceptual stage of the design workflow (10). The acoustic performance at thisphase is mainly digitally tested by limiting the prototyping costs. The following steps are suggested(Figure 4):(i) Different geometric design rules are used based on those introduced here in Section 2 in orderto maximize the scattering coefficient and improve the uniformity of the reflections spatial
distribution The geometry of the bases is a Voronoi function that allowed for a randomized structureof the elements. The coverage density, height and dimension of the elements are varied using four
attraction points. Further, the entire surface is intersected with a curved profile for a more spatialreflection distribution uniformity. (ii) A Computational Design System is built with two clusters, thatare the Geometry Generation and Acoustic Analyses clusters. The first cluster uses Rhino andGrasshopper for the parametric modelling. The second cluster uses an ad hoc script integrated in thefirst cluster and informs it on the acoustic performance based on a first qualitative approach that islater integrated with a quantitative one that uses Pachyderm Acoustics. (iii) The optimized surface isthen 3D printed through a Makerbot Replicator 5th generation using PLA. Since the 3D printing
required a very long production time, a plaster 1:5 model of the complete sample was produced foracoustic measurements. (iv) The surface is characterized from the scattering coefficient point of view
based on ISO 17497-1 measurement approach. The data are used to inform the Geometry Generation
cluster.

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5. CONCLUSIONSThis paper has analyzed different studies, which have investigated the diffusive surface based on
the ISO 17497-1 standard. The aim was to analyze the geometrical rules tested in each experiment inorder to give useful and simple guidelines to designers for the optimization of diffusers performance.
Further aspects could be investigated through BEM or FEM simulations in a more systematic way infuture work. Four case studies related to the design workflow of diffusive surfaces have be encompared in terms of design workflow. The analyses showed that besides the need for more insighton the performative effects of geometrical rules, there is also a need for a complete computation design
system that could host different digital tools: Geometry generation, Performative analyses and Robotic
simulation. These tools could be improved by a more careful attention towards a more user-friendly
approach based on a proper user-interface and rapid visual performative feedback.
The design of special patterns of reflection and potentially other unconventional acoustic surface
such as metamaterials behaviors can be investigated in similar ways. The design process of diffusive
surfaces shows, that raising awareness among architect and designers related to the correlation of theperformative output and geometrical rules, could lead to a more conscious and efficient design of theentire space.

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