ISRA2013

Toronto, Canada

International Symposium on Room Acoustics 2013 June 9-11

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Integration of acoustics in parametric architectural design

Dr Thomas Scelo (tscelo@marshallday.com) Marshall Day Acoustics Hong Kong SAR People’s Republic of China

ABSTRACT

The integration of basic geometrical acoustics into architectural design is not new. The arrival of 3D modelling packages such as Grasshopper and Maya has certainly increased the consultants’ efficiency, the dialogue within the design team and propelled a new generation of architects into glamorous spheres. But it has also, thankfully, forced the consulting profession to go back to the basic. Efficient algorithms are complex and their development time consuming. At first, Grasshopper’s apparent limitation in complex calculus seems to confine its use to basic trigonometry. In many ways, our parametric contribution was not more evolved than that of our predecessors, it simply is virtual, tri-dimensional and in real time. Much has been said about geometry analysis including 1st and 2nd order reflections, reflector coverage, delays and energy density. However, little is discussed about actual parametric design. Recent collaborations with architects well versed in parametric design have offered us the opportunity to translate conceptual acoustic considerations into real input parameters for the automated generation of rooms. In more technical terms, Grasshopper and Maya are used to resolve inverse problems for which the output is assumed. The unknown to the problem is the ‘transfer function’, for which one geometry is built for a given source and receiver locations. This paper describes the collaborative approach to develop a single algorithm for both acoustic and architectural form generation.

1 INTRODUCTION

In the recent years, a new generation of design tools have emerged from the ever evolving architects’ 3D computer aided arsenal. Acousticians have inevitably been introduced to these and many of us have seen some benefits in adopting the same language as our clients. To each his/her interest and needs. For Marshall Day Acoustics, parametric tools do not aim at replacing the well established and tested ray tracing packages (Odeon, CATT, Matlab). Instead, they represent a mean to further enhance our collaborative approach by creating interactive and visual tools to assist us during workshops with architects. Should they be seen as replacement, it will be that of study cardboard models, scissors and tape traditionally used at the early concept stages.

Plans, sections, rulers and sliding rules are perfect design tools8 as long as the architectural concept is wholly represented in 2-dimensions. Modern architecture often challenges this and 3D computer packages are increasingly the only possible visualisation medium. A parametric acoustic design tool should therefore provide detailed and accurate acoustic information but

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maybe more importantly it should be a visual aid to the architect. If the architect does not visualise positive improvements to a geometric change, he has no reason to accept the change.

Such a tool should also provide us with a wide range of possibilities. Many projects seek to deliver a new architectural paradigm. How can a geometry-based algorithm be flexible enough to allow manipulation of elements and surfaces from one project to another?

Figure 2: Example of performing arts venues where 3D computer model are required

(copyrights Zaha Hadid Architects)

Our journey through the development of parametric tools has just started. This paper aims at summarising where we started, what we have achieved to date and, more revealing, where we are going.

2 RAY TRACING

Ray tracing was the first obvious stage of utilisation of parametric design tools. From the simple 1st order reflection coverage including:

• Time delay and energy level with respect to the direct sound

• Energy with respect to the reverberant field

• Angle of arrival to the listener

• Frequency dependence of reflection energy as a function of the reflecting surface dimensions.

Figure 3: Relevant information on rays can be provided using text tags or colour coding

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As always, once an algorithm is developed, one quickly identifies its limitations. In our case, it was the 2nd order reflections in a 3-dimensional world that were the first necessary improvement.

Figure 4: Input parameters can also be used for the 2nd order reflections

Figure 4 illustrates how a ‘cornice’ 2nd order reflection can be optimised using basic orientation parametric controls. In this case, the simple operation was to rotate the individual reflectors about their 2 main axes.

3 3D OBJECT MANIPULATION

Beyond the simplest rotation of a reflector about arbitrary axes, as shown in Figures 3 and 4, we aim to use the same geometry building ability of Grasshopper that seduced the architects and designers in the first place.

Extending the algorithm to create a reflector, as opposed to building a hard to control one in Rhino, can be achieved using the already existing functions in Grasshopper. This lifts the reliance on less flexible Rhino elements. For example, Grasshopper objects allow us to quickly determine the necessary curvature to ensure appropriate coverage of an audience area. In comparison, manipulating Rhino objects requires rebuilding curves, edges and NURBS without the possibility of a real-time assessment.

This is particularly useful when the reflecting surfaces are curved. Indeed, flat reflectors do no always complement a curved architectural language, so why should be use them during architectural design workshop? In addition, they are not the most efficient sound reflectors, as their coverage tends to benefit only few seats. If in addition, they are closed to the audience, image shift and coloration can occur.

So the next improvement in our parametric toolbox was to provide a mean to control the curvature of any reflector (even those extracted from curved geometries) so that it can embraces the architectural language, provide better reflection coverage and soften strong reflections.

Figure 5 shows a simple curved reflector above an orchestra pit generated directly in Grasshopper. The associated set of ‘curvature control’ parameters allowed us to quickly determine the appropriate geometry for speech support and communication between the pit and the stage.

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Again, the above design efforts were based on an assumed geometry, or at least an assumed position for the geometry. Although very efficient and useful, this remains a passive design tool.

Figure 5: Reflector generation and curvature control in Grasshopper.

4 INVERSE PROBLEM ANALOGY

We are very fortunate to regularly work with outspoken advocates for parametric design. When architects come to us and asked us for assistance with a parametric design of a performance venue, we sew an opportunity to experiment and develop. But this opportunity should not be exclusive to the acoustician, but to the entire design team.

The analogy with an inverse problem often springs to mind. Indeed, the passive review of a room geometry and shape invariably starts from the source, reaches a surface in the room and assesses where, when and in what conditions it lands. We proposed inverse the two last operations:

1. We know where a listener is located 2. We know where the source is located 3. Can we generate a surface to connect, via a reflection, the audience with the stage?

This is not an inverse problem in the mathematical sense, because it is well known that there is not a unique but an infinite number of solutions to the above question, luckily. Yet, one of these solutions can be developed when we introduce, in addition to our selfish acoustic requirements, those borne from architectural, aesthetics and theatrical considerations. It is by nature, a collaborative approach.

• The starting point is of course the stage and the musicians, and more precisely what is generated on it. In our analogy, we would call this input parameter to our problem. By respect to the musicians, we note this [ M ]

• The impulse response of the room is applied to the sound emitted on the stage and results in the objective (and subjective) experience at the listening position. We limit for now our consideration to the early part of the room response, and more precisely to the sequence of early reflections reaching the listener. The operation that transform the source into the received sound remain a characteristics of the acoustics of the room. We note it [ A ]

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• The result from the room operation [ A ] on the input variable [ M ] is what we define as the sequence of discrete early reflections [ D ]. In our case, these are known parameters

• Finally, each one of team member (architect, theatre consultant, A/V consultant8) has its own practical requirements. For example, we need lighting positions and follow spots that are appropriately located in the room. In our analogy, these constitute the ‘boundary conditions’ of our problem that help us narrowing down the infinity of solutions to our problem.

We stress that this analogy does not aim to resolving the impulse function of the room, but only the sequence of early reflections serving a given audience block. No consideration has been made for crucial parameters such as room volume, absorption, diffusion other than those inherent in the architectural forms.

The problem can then be written as follows:

��� = ������ leading to the solution �������� = ��� (1)

This is most likely a ill-posed problem. Indeed not all variables are independent, the relationships between these variables are not all linear and we have sometimes more observations than unknown (unless each seat has its own set of reflectors). If the problem could truly be written in a correct matrix form, the matrix [ M ] would almost never be square and an objective function will be required.

In addition, the ‘boundary conditions’ as defined by, for example the architect or the brief, can introduce more variables or eliminate some. For example, certain designs invariably link the early and late acoustic responses of the room. In this case, the assumed reflection sequence cannot easily be dissociated from the volume, width and height of the room.

Finally, the matrix [ M ] is unlikely to be square and consequently hard to inverse. But we still make the analogy because we start from the observation of a sequence of reflections and work back to the primary geometrical features responsible for it.

5 BASIC ACOUSTICAL CONCEPT

In a 2-dimensional world, a sound reflection path can be inscribed into an ellipse, the foci of which are the source and receiver points. If we limit our analysis to ray-tracing, any single reflection in any 3-dimensional room can be represented by a point on such ellipse.

The characteristic dimensions of the ellipse define the path length difference and therefore the time delay and part of the energy level of the reflection. A direct inverse relationship can therefore be established in the visual context of Grasshopper where the time delay is set as input parameter and the ellipse dimensions are only the result of simple geometrical calculus.

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Figure 6: Time Delay as an input parameter in Grasshopper (top: 30ms, bottom: 55ms)

In a 3-dimensional world where the subject is not a ray but a sound wave, and where we are considering more than one ray at a time, we need to extend the concept from an ellipse to a 3-dimensional ellipsoid.

Figure 7: All points on the ellipsoid provide reflections with identical time delay

To ensure that the reflection reaches the listener with a lateral incidence to favours envelopment (apparent source width), one cannot assume that all points on the ellipsoid are valid reflection positions. A control parameter needs to be created to measure the angle of incidence and narrow down the set of possible reflection points.

Figure 8: Truncated ellipsoid to ensure lateral

6 IMPLEMENTATION

6.1 Architectural and theatrical input

The close links between architecture, acoustics and theatre design are as important at the design phase as they are during the operation of acousticians are often presented with a respected and made the work acousticallyparameters to our design.

In a recent case, the vision could be grossly summarised room finishes and a seating layout (plan and elevation).

Figure 9: Concept for a grand auditorium where infinite loops define the architectural language

The seating layout imposes a set source positions and types of source.

In addition, technical requirements for sightlines, lighting angles and positions are key to the function of the space. Once expressed by the theatre consu

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Truncated ellipsoid to ensure lateral incidence with respect to the listener

Architectural and theatrical input

The close links between architecture, acoustics and theatre design are as important at the design phase as they are during the operation of the built venue. At the concept

presented with a ‘vision’ that expresses an architectural language respected and made the work acoustically. This sets important boundary conditions and input

could be grossly summarised to the architectural language for the eating layout (plan and elevation).

Concept for a grand auditorium where infinite loops define the architectural language

The seating layout imposes a set of receiver positions while the project brief impsource positions and types of source.

In addition, technical requirements for sightlines, lighting angles and positions are key to the function of the space. Once expressed by the theatre consultant, these become another set of

espect to the listener

The close links between architecture, acoustics and theatre design are as important at the venue. At the conceptual stage,

an architectural language to be boundary conditions and input

rchitectural language for the

Concept for a grand auditorium where infinite loops define the architectural language

of receiver positions while the project brief imposes a set of

In addition, technical requirements for sightlines, lighting angles and positions are key to the ltant, these become another set of

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boundary conditions. In ideal cases, these conditions can be turned into modifiable parameters or part of the unknown to the problem.

Figure 10: Basic concept layout that defines the set of audience blocks and input parameters for lighting. In between these is the realm of the acoustician

6.2 Acoustic input

From a room acoustic point of view, it is not a ‘desired impulse response’ that we seek, but a sequence of early reflections. Each reflection is defined by a time delay, an energy level and a direction of arrival. As a principal guide for design, we aim at achieving at least 3 first order or ‘short’ second order early reflections to each listener to ensure sufficient clarity, envelopment and early source strength.

Given that the energy level of a reflection is a function of the path length difference between direct sound and reflected sound, if we assume that the finishes are defined and known (material and presence/absence of diffusion treatment), the three characteristics for each reflection can be reduced to 2 independent variables: path length difference and direction of arrival.

An algorithm was first developed in Grasshopper to generate the 1st acoustic input parameters: regions in the 3-dimensional space where reflectors can be located (truncated ellipsoids).

Figure 11 illustrates a set of reflectors developed for a set of lighting positions. Because the truncated ellipsoid approach offers several possible positions for a single reflector, the set shown here only constitutes one possible solution. Depending on the constraints introduced by the other input parameters, another set can be generated.

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Figure 11: One possible acoustic solution

We note that the actual acoustic input parameters to our algorithm are not the reflectors themselves but those required to develop 3 truncated 3D ellipsoids per audience block. From these, the reflectors are generated, moved and combined according to the boundary conditions.

6.3 The outcome

Once all the input parameters are set, the ‘routine’ can start where one change to the source [ M ], the reflection sequence [ D ] or the boundary conditions lead to a new geometrical solution. Figure 12 illustrates the first built mesh.

Figure 12: First parametric shell generated using Grasshopper in Rhinoceros

Although started as a Grasshopper routine, the core of the algorithm was later translated and integrated to a Maya script. Maya offers less user-friendly scripting abilities but allows better geometrical control of the surfaces. The control points of the large shell can be directly manipulated while the script ensures that no conflict with the input parameters exists.

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Figure 12: Simplified shell in Maya that better meet the boundary conditions

Unfortunately, the benefits in terms of geometry control provided by Maya had a cost as only basic real-time ray-tracing could be added to the script within the timeframe of the project.

Figure 14: Basic real time ray-tracing in Maya during the model manipulations

7 CONCLUSION

Multiple iterations of the design have been required to accommodate the ever evolving design details, as well as the many other requirements that were not included in the algorithm.

As mentioned in the introduction, the parametric design tool presented here does not aim at replacing the existing and well known ray-tracing packages. All major iterations of the developed

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shell have been imported into Odeon and simulations have been run. There are, to our knowledge, no Grasshopper/Maya algorithm that yet can handle a large enough number of rays to accurately estimate objective acoustic parameters and generate reasonable impulse responses for convolution.

However, the Odeon simulations have shown that the design has been very significantly improved in the process presented herein while maintaining the architectural concept. It has also provided tremendous opportunities to better understand the architectural concept while halving the time spent on 3D file manipulation duration of the schematic and detailed design phases.

Figure 15: Before (top) and after (bottom) parametric optimisation of the architecture / acoustics / theatre design

ACKNOWLEDGMENTS

We gratefully acknowledge Sir Harold Marshall for bringing our attention to the ellipse (amongst many other things) and to Zaha Hadid Architects, in particular Simon Yu and Uli Schifferdecker for the very stimulating workshops.

REFERENCES

1 Michael Barron, “Auditorium Acoustics and Architectural Design”, 2nd edition, E & FN Spon, 2003.