Think script build

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Rasmus Holst s061860
M.Sc. Architectural Engineering
think, script, build
Architectural engineering through parametric 
modelling of intelligent systems in architecture.
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Resumé |
This is a project about programming of intelligent systems by implementing 
information of physical behaviour, material-properties and connection design 
regarding advanced architectural projects.
Focus is on utilisation of the geometric behaviour of elastic elements in con-
nection with deformation for optimization, fabrication and inspiration. The 
purpose is to create a process from ideas on sketch to a realizable project 
through scripting, parametric design and algorithmic modelling.
The motivation and inspiration for this project are the smooth shapes that 
come from bending and deforming simple elements. Furthermore, the fact 
that these shapes come from the very nature of minimizing internal potential 
energy, makes this approach very interesting in terms of both architecture 
and engineering.
Scripting and parametric modelling allow for generation of complex geometry. 
In combination with engineering knowledge of geometry, material behaviour, 
constraints, external influences etc., parametric design is a great source of 
opportunities to fulfil creative ideas.
Almost everything can be generated digitally and digital fabrication allows 
for production in most cases. However, sometimes these procedures become 
costly, material intensive and therefor often not sustainable. When an ad-
vanced shape needs to be cut out of sheets or blocks, there will be material 
waste, some of which can be recycled, however, this also uses energy.
By thinking and scripting, complex and optimised projects can be built simply 
and sustainably. This thesis aims to demonstrate how.
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Title sheet
DTU - MSc. Architectural Engineering
Master thesis - Autumn 2012 (E12) - 30 ECTS Points
Subjects:
 Architectural Engineering
 Parametric design
 Optimization
Supervisor:
 Henrik Almegaard - DTU - hal@byg.dtu.dk
Business partner:
 Henning Larsen Architects
 Jakob Strømann Andersen - JSTR@henninglarsen.com
Project period:
 The project work is carried out during the period from 
 03.09.12 - 25.02.13. This period includes 3 weeks of vacation.
Hand-in:
 25.02.13
All rights Rasmus Holst, Autumn 2012.
Thesis done by:
Date: Signature:
Rasmus Holst, s061860
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Preface
This thesis is the conclusion of my Master program in Architectural Engineer-
ing at the Technical University of Denmark (DTU) 
At the beginning of this thesis the direction was set out by the belief that a 
combination of curiosity, programming skill and craftsmen experience held the 
potential of interesting and optimised design.
The amazing collective around the parametric forum of Grasshopper3d has 
been an amazing resource. Especially the likes of Daniel Piker (Kangaroo), the 
team behind Karamba3d and many others have been very helpful and inspi-
rational. 
The collaboration with Henning Larsen Architects has proven very interest-
ing and useful. Especially thanks to Jakob Strømann-Andersen who has been 
great at putting my solutions to the test in ongoing projects. Also thanks 
to some really nice colleagues and to the entire firm for setting me up with 
computers, software, modelling room, laser cutter, printers etc. 
Last but certainly not least, a big thanks to Henrik Almegaard for great 
guidance, advice and inspiration throughout this project and my entire study 
time at DTU. 
It has been very interesting doing this thesis and I hope that you will enjoy 
reading it as much as I have enjoyed working with it.
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Report layout
This report is divided into 8 chapters.
Firstly an introduction to the thesis problem statement, motivation and meth-
od are given. To guide the reader through the process of this project, the 
report is set up in more chronological order than the actual iterative process. 
This way chapters 1-2 introduces the thesis and the principles of parametric 
design. Case[0] in chapter 2 exemplifies parametric design in action. 
Chapter 3 is an initial research into structural principles from simple ele-
ments. This sets up an outline for overview and inspiration. One principle is 
chosen for further investigation in the following chapters. (think)
Chapter 4-6 sets up the theory of physical modelling and investigates script-
ing results. The method build in chapter 4 and 5, is tested on Case[1] in 
chapter 6. (script) 
Chapter 7 goes through the final case work, using the theory, methods and 
scripts build through the project in case[2]. The case is a pavilion design and 
focus is on fabrication and build ability. (build)
Finally chapter 8 reflects upon obtained results and perspectives.
When ever this logo is shown close to an illustration, a corresponding anima-
tion can be found on www.vimeo.com/rasmusholst/albums. Click on the album 
“Think, Script, Build”.
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1
2
3
4
5
6
7
8
think
Introduction
Case [0]
Initial research
Modelling
Investigation
Case [1]
Case [2]
Reflection
script
build
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table of contents
1 Introduction page 16
1.1 Architectural engineering 16
1.2 Historical perspective 16
1.3 Parametric design 18
2 Case [0]: EPO page 26
2.1 European Patent Office - Introduction 26
2.2 Parametric facade design. 28
2.3 Optimization 30
2.4 Scripting 32
2.5 Parametric studies 34
2.6 Discussion 38
2.7 Perspective 40
2.8 Part conclusion 42
3 Initial Research page 46
3.1 Simple advanced structures 46
3.2 Gridshells 64
4 Modelling page 68
4.1 Paper play 68
4.2 Theory 70
4.3 Physical modelling 72
4.4 Definition breakdown [Spline] 76
4.5 Plate modelling. 78
4.6 Connection modelling 87
4.7 Definition breakdown [Mesh] 90
4.8 Part conclusion 92
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5 Investigation page 96
5.1 Jukbuin pavilion 96
5.2 Jukbuin pavilion - Script 100
5.3 Jukbuin pavilion - Build 130
6 Case [1]: Nordea Bank page 134
6.1 Nordea bank ørestad - Introduction 134
6.2 Method 136
6.3 Form studio 138
6.4 Example 140
7 Case [2]: Pavillion page 166
7.1 Introduction 166
7.2 Concept 168
7.3 Form studio 170
7.4 Structure 172
7.5 Fabrication 174
7.6 Part conclusion 176
8 Reflection page 180
8.1 Discussion 180
8.2 Perspective 182
8.3 Conclusion 184
9 Bibliography page 186
9.1 Resources 187
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Background
Background
The digital age has given access to tools for architects and engineers that 
allows for creation of complex geometry and advanced systems. At the same 
time there is a great demand for affordable solutions, sustainability and 
optimization. 
In the process of optimization one looks for the best solution of weighted 
parameters within a given space of solutions. When it comes to efficiency of 
buildings, there is a great geometrical challenge for the architect and the 
engineer in choosing the right solutions from the beginning. 
Parametric design
In a design process, the solution space within the concept is often endlessly 
large. This gives thousands of possible combinations of angles, lengths, 
heights etc. The normal procedure is to boil this solution space down to a 
few proposals, chosen on the basis of intuition, aesthetics, analysis and/or 
experience. 
Scripting allows for designing parametrically, which enables the setting up of 
intelligent systems. These systems become intelligent by adding information 
to geometry, often points, nodes and lines. Through iteration processes, in 
which equilibrium of the stored information in the system is searched for, the 
system becomes self-emergent*. In some literature this is compared to ant 
hills, mouldfungi, bird flocks and schools of fish. Here each individual has 
a simple local knowledge about its needs and tasks. This is what makes the 
global system work and achieve its goal. This theory of self-emergence is a 
matter of big discussion, research and investigation.
The basic insight in this phenomena, “wisdom of the crowds”, is in short that 
useful informations can be obtained via many shots in the dark. Scripting 
allows the designer to make the computer go through many solutions and 
output wanted results and consequences. 
* Emergent - Developing. Under development.
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Mimicking nature
As engineers we are used to analyse proposals for structures of different 
kinds. That being energy efficiency of facades, structural behaviour of build-
ing elements etc. We have to predict the output of our project before it is 
build. For centuries theory has been built on this subject, and there is a lot 
of methods and software that help us predict consequences of more and more 
advanced systems. 
When it comes to structural performance we usually take our starting point 
in the un-deformed state of elements. One exception is the prestressed 
concrete beams and slabs. The prestressing has the advantage of creating 
opposite stresses to those coming from imposed loads. Therefor it increases 
the element performance, while it decreases the resource usage.
Maybe the reason why engineers and designers do not utilize this behaviour 
more, is the complexity that lies behind the bending and twisting of elements. 
Mostly we strive towards linearity, planarity and thereby try to avoid bend-
ing, all the while the design of architects tend to get more organic. At the 
same time it is known that simple non-rigid elements can gain stiffness from 
deformation into double curvature. 
By setting up an intelligent system, using scripting, it is possible to mimic the 
behaviour of these elements and to setup tools for form-finding, simulation 
and analysis. 
Form finding
Form finding is the abstract modelling of material organisations as the active-
ly negotiate internal and external influences. These can be laws of physics as 
well as architectural affect, spatial requirements and performance demands. 
The traditions has a long history that stems not only from the physics, but 
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also from the desires of designers and engineers to invent and innovate 
within the space of possibilities. Amongst others in this history is the in-
vention of a description of the catenary curve and the reciprocal funicular 
curve by Antonio Gaudi, used for designing compression only structures. Frei 
Otto’s study and abstraction of tendencies and behaviours of minimal surface 
organisation found in soap film, led the way to novel knowledge of membrane 
structures. The expansive learnings of Frei Otto’s distillation and abstraction 
of materiality has also enhanced the knowledge and ability to design large 
span shell, lamella and lattice structures, even though they are constructed 
from seemingly contradictory materials. 
Algorithm
Knowledge of a given material’s properties and/or molecular anatomy needs 
to be established as a computational description of the self-organisation. In 
Frei Otto’s soap film the setup can be understood as the process of one 
molecule acting upon another while negotiating influences. 
A contemporary method is the use of particle-spring systems that digitally 
simulates soap film structures. In terms of architectural geometry, such as 
surfaces, volumes etc., it is represented as a network of particles hitched 
to one another by springs. Equilibrium is found via numerical iterations. Two 
common strategies are dynamic relaxation or the force density method. Both 
uses the mathematics of Hooke’s laws of elasticity. The algorithm allows for 
implementing architectural schema also. Such as to define for example the 
front door. This becomes another layer of influences or motivations that is 
to be negotiated within the system. Digital form finding is not to replicate the 
work that has preceded it, but rather to seek out new territories.
Wood
These methods can be used to describe many different materials and be-
haviours. The focus of wood in this thesis is purely a case of interest and 
admiration of the sustainable, flexible and aesthetic nature of the material.
Fig. 2 Gaudi chain model
Fig. 3 Frei Otto - Optimized path 
experiments
Fig. 4 Wood materiality
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Problem statement
How can parametric design be implemented in an architectural design process 
and become added value in terms of modelling speed, time, analysis, optimiza-
tion and development.
From this perspective, the intention of this project is to discover if and how 
we can use simple, regular building elements in the construction of the in-
creasing numbers of complex shaped architecture projects.
The solution to this problem is interesting to all parties in a building pro-
ject; designers, engineers, investors, entrepreneurs and so on, in terms of 
economy, optimization, sustainability and build-ability.
The title of this report - think, script, build - is the short description of the 
approach that will be taken in discovering the above problem: How can script-
ing be used to simulate the deformation of simple elements and networks and 
thereby become a tool for form-finding, analysis and building descriptions of 
complex geometries.
The interdisciplinary method of architectural engineering will be used in com-
bination with parametric modelling of digital systems, that become intelligent 
by scripted information, for architectural projects. 
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process | disposition
Method
At the beginning of the research, this project looks at interesting structures 
and principles of more or less simple and regular elements. An outline of this 
initial research is set up for inspiration and overview. One of these principles 
are chosen for more thorough explorations within the think, script, build ap-
proach.
To begin with, an introduction to parametric design and scripting is given by 
brief explanation and exemplification through case studies together with Hen-
ning Larsen Architects. By doing so, common ground for further collaborative 
investigations are established. Then the script for parametric design of the 
chosen structure principle is build in an iterative process consisting of theory, 
exploration/experimentation and casework. 
The idea behind think, script, build is to set up an effective and interactive 
workflow between the three parts. This means working in and out of the 
computer, sketching and creating ideas, scripting and building digital paramet-
ric models.
The building of the parametric model strives towards real time user control, 
simulation and analysis. To be able to analyse the model real time and find 
responses to any changes made, the model is linked with internal and external 
calculation engines. 
The chosen main software is Rhinoceros3D, from Robert McNeel & Associ-
ates, a 3d modelling software with many plugin and extension possibilities. 
Grasshopper3d is a visual programming language plugin for Rhinoceros3D, 
developed by David Rutten. Grasshopper3d also implements more common 
scripting languages, such as Python, VB, C# etc, as well as many application 
plugins for different use.
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Summation of method:
- Introduction to parametric design.
- Gathering of construction principles
 - Wood structures.
 - Aggregate/module structures
 - Newer installation structures.
- Buildingof script(s).
 - Theory: Materials, properties, physical model.
 - Experimentation and comparison
 - Connections
 - Intelligent system.
 - Linkup with other analysis software
- Implementation.
 - In collaboration with Henning Larsen Architects method and 
 principles are tested on case studies of competetion projects. 
- Model/pavilion
 - Building of 1:1 scale model.
The described method is not chronological, but should be seen as an itera-
tive process. This process is illustrated as the time line on Fig. 5 setup at 
beginning of this thesis.
study
theory test/explore
case01 case02 case03 writing conclusion
theory test/explore model
paper
september october november december january february
1:1 part
model
report
Preliminary time schedule - proces
2013
AAG12 Conference and Solar decathlon: 
25.09.12 - 08.10.12
Fig. 5 Preliminary timeline
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[INTRODUCTION]
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[Architectural engineering] + [Parametric design]
Rhino Grasshopper
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1 | Introduction
1.1 Architectural engineering
1.2 Historical perspective
Architectural engineering is intended to bridge the gap between architects 
and engineers. Meaning that the architectural engineer is involved in the 
project from the early design stages, working closely with the architect 
to evaluate and contribute in choosing the best solution of a given design.
“The role of architectural engineers can overlap with that of the archi-
tect and other engineers. Like architects, architectural engineers seek to 
achieve optimal designs within the overall constraints, but mainly use engineering 
tools to attain their goal.” (DTU MSc. Architectural Engineering 2012)
Using the technical knowledge in a creative way is meant to lift the archi-
tectural visions in a way that optimise and implements the ideas of the ar-
chitect. In doing this, one strives towards creating a fusion between art and 
science. Early considerations of structural behaviour, energy consumption, 
material etc. helps in optimising the design. Small changes to the geometry or 
materiality, can have a big impact on the structure, amount of daylight, heat 
transfer, build-ability etc. There are many parameters to adjust and therefor 
an almost endless amount of solutions. 
Parametric design allows changing parameters of the project and quickly 
review the consequences without having to redo everything. This becomes 
the ultimate tool for architectural engineering, combining aesthetics, sci-
ence, math and analysis in the same model. Every change made to the design 
has an impact on the performance and can easily be reviewed real-time.
A significant inspiration for this mentioning of architectural engineering are 
the likes of important people, amongst others Antonio Gaudi, Mies van der 
Rohe, Buckminster Fuller, Pier Luigi Nervi and Frei Otto. Each of them combin-
ing arts and sience using different approaches. 
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Fig. 4 Frei Otto
1.2.1 Mies van der Rohe and Bauhaus.
Ludwig Mies van der Rohe was one of the three architect directors at Bau-
haus. The German school combined crafts and the fine arts and became one 
of the most influential currents in modernist architecture. One of the main 
objectives of this school was to unify art, craft and technology. 
1.2.2 Buckminster Fuller and the Dymaxion World.
Richard Buckminster Fuller spent his life working across multiple fields, such 
as architecture, design, geometry, engineering, science and education. He 
described himself as “a comprehensive anticipatory design scientist”*. The 
concept of Dymaxion - DY-namic, MAX-imum, tens-ION is the idea of the most 
efficient overall performance per unit of input. 
1.2.3 Pier Luigi Nervi
Italian architect and engineer who did great innovative research in applica-
tions of reinforced concrete structures, especially working with thin shell 
structures. He stressed that intuition should be used as much as mathematics 
in design. Like Heinz Isler, Felix Candela and Eduardo Torroja, Nervi looked 
towards Gaudi’s funicular models.
1.2.4 Frei Otto
Frei Otto is the leading authority on lightweight tensile and membrane struc-
tures and has pioneered the advances in structural mathematics and civil en-
gineering. His work on optimization of structures and formfinding by looking at 
nature, is still a great inspirational source in the parametric environment. ** 
Common to them all is that they are working with the beauty within knowledge 
of science. This enables them to work and design across multiple fields and 
thereby create interesting and optimised structures. However, they did not 
have the same access to digital tools and emerging technologies as we have 
today, therefor it is interesting to look at future developments of their ideas 
and knowledge.
* http://bfi.org/about-bucky
** Finding From - Frei Otto (1996)
Fig. 1 MIes van der Rohe
Fig. 2 Buckminster Fuller
Fig. 3 Pier Luigi Nervi
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1.3 Parametric design
Fig. 5 space ruler.png
1.3.1 What is parametric design?
When googling the word “parametric design”, it is one of the few searches 
where the first hit is not a wikipedia explanation. This is probably because 
their is no precise definition, rather there is a lot of related terms; genera-
tive design, algorithmic design, node-based design, logical modelling, program-
matic modelling etc. But these notions are not very good and a bit latent 
- basically it is a far more sophisticated way of modelling digitallly.
Many times when modelling a concept, often certain operations are monotone 
and repetitive, operations that can be considered as algorithms. A good exam-
ple of such is the “array” tool in most CAD software* - a way to repeatedly 
move and copy elements. The physical aid of “array” would be the Linex line 
spacer (Fig. 5). Instead of doing it manually and use time on drawing, erasing 
and redoing, we can use the abilities of computers to work with algorithms.
Imagine that you are drawing the facade of a skyscraper. Each floor has 8 
windows, divided evenly along the length of the facade. It is simple, but after 
drawing it in the morning, you find out that you need bigger windows, then you 
find out that you need more windows, then the facade size is decreased, then 
it is rotated, then skewed - with maybe a thousand windows, you are going 
to use a lot of time. Algorithms will make the computer do your calculations 
and draw your geometry. 
Making the computers do your calculations and run algorithms has been 
around for a long time. Describing rules for geometry started with Euclid 
approximately 300bc. Far back the first calculator, the abacus, is believed 
to have been used. The age of computation started when William Shockley 
invents the transistor in 1947. This leads the way to circuit boards, electronic 
calculators and computers.
* CAD - Computer aided design.
introduction
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300 BC: Euclid - Elements.
500 BC: Ancient greek Abacus. 
1947: William Shockley invents the Transistor.
1963: Ivan Sutherland writes SketchPad. Graphics.
1977: Dassault wirtes Catia. 3D drawing
1978: Hewlett Packard - First PC’s.
1982: Autocad first release.
2008: David Rutten invents Grasshopper3d. 
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The concepts of the abacus and the knowledge of Euclid was combined by Ivan 
Sutherland in 1963, when he wrote the first CAD-application SketchPad, where 
the designer interacted with the computer graphically by using a light pen to 
draw on the monitor. SketchPad evenincluded a solver that allowed assigning 
constraints, such as lines being individually perpendicular**. 
Ivan Sutherland described himself as being a visual thinker, therefore he had 
his interest in computer graphics, saying: “...if I can picture possible solu-
tions, I have a much better change of finding the right one.”***
In the late 1970s simpler operating systems and the release of desktop com-
puters encouraged engineers to experiment with programming and became the 
start of workstation computing. The development in CAD grew fast during 
the 1980s, during which the software Pro/Engineer (1987) by PTC and more 
famously - AutoCAD (1982) by Autodesk was released. In 1992 the McNeel 
group integrated their NURBs geometry library in AutoCAD and in 1994 McNeel 
released the first beta version of Rhinoceros3D (Rhino).
Pro/Engineer (1987) was the first software to fully implement the concepts 
of SketchPad (1963), where constraints and solvers created the basis for 
parametric design. FInally in 2008 David Rutten invents Grasshopper for Rhino
Programming and finite element analysis has been used for a while by engi-
neers, but the visual programming interface of the plugin Grasshopper for 
Rhino has taken programming to a familiar place and this has created a com-
mon playground for architects and engineers. 
In the following, the use of Grasshopper will be explained. 
** SketchPad on youtube: http://www.youtube.com/watch?v=mOZqRJzE8xg
*** Ivan Sutherland. http://history-computer.com/ModernComputer/Software/Sketchpad.html
Fig. 6 SketchPad Demo (1963)
introduction
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“Hello John. We are going 
to show you a man actually 
talking to his computer.” 
 
- Prof. Steven Coons, MIT (TV Show 1963).
“..if I can picture possible 
solutions, I have a much 
better change of finding 
the right one.” 
 
- Ivan SUtherland
Fig. 7 Youtube - Skethcpad demo
Fig. 8 Ivan Sutherland
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1.3.2 Rhino + Grasshopper
Grasshopper was written by David Rutten in 2008 for McNeel. David studied 
architecture at TUDelft, where he got tired of the lack of scientific approach 
in design. All designs where based on emotional or philosophical considera-
tions. He wanted to see numbers and proof that some solutions where better 
than others. Similarly to the likes of Frei Otto and Nervi, he implements tech-
nical knowledge as well as emotions, philosophy in the evaluation of design 
using Grasshopper. There are many different descriptions of Grasshopper; 
a visual algorithmic interface, visual programming, Visual Basics without the 
Basics and many more. 
Briefly how it works : There are two basic elements - data 
and actions. Every step of connecting components is like lines 
in a source code, except there is no code. All boxes can be 
considered to represent small pieces of code. As with cod-
ing, all commands take inputs and creates output through the 
requested action. These Grasshopper scripts will be referred 
to as definitions throughout this report. 
This method is very handy in speeding up the drawing process and having 
ultimate precision, but it is the access to all data, that makes it really inter-
esting. Especially for engineers, treating the data mathematically has a great 
potential. Similarly to the visual approach of Ivan Sutherlands (cf. p. 20), 
Grasshopper enables real-time visualization of solutions and consequences 
and it thereby becomes a great media within a competition team. 
1.3.3 Parametric design in action.
So apart from drawing spheres on a line, how is parametric design an added 
value to an architectural company like Henning Larsen Architects? The thesis 
statement is that parametric design will speed up the modelling processes. It 
might take longer to set up a good script, than doing the first drawing. From 
Fig. 9 Points + line comp.
DATA ACTION
Fig. 10 Step 1. Pts + line
Fig. 11 Grasshopper Infacade. Rhino Viewport
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DATA ACTION
DATA
ACTION
Fig. 12 Step 2. Divide line Fig. 13 Step 3. Draw spheres
here on however, the script will create changes within seconds.
On top of this, the open platform, that Rhino3d and Grasshopper is build upon, 
enables linking the model with analysis tools for optimization of e.g energy 
use and structural efficiency.
1.3.4 Software confusion
Because this thesis is based on a modelling software, Rhino, the Grasshop-
per plugin and plugins and extensions for Grasshopper, it is very easy to be 
confused as a reader. Therefor explanation icons will be presented at the 
introduction of each chapter. The plugins for Grasshopper are really impor-
tant as they add different extended abilities of the scripting interface. All 
extensions will be explained when used, but here in bulletform:
[DIVA]
[Karamba3d]
Rhinoceros: 3D modelling software. Basis for modelling. 
 The builder.
Grasshopper3D (GH): Visual scripting interface plugin. 
 Tells the Rhino what to do.
Python: Scripting language plugin for GH. Intelligent helper 
 for the Grasshopper. (Mentioned Python scripts are coded by the author)
Kangaroo: Physics engine plugin for GH. 
 Simulates physical behaviour for the Grasshopper.
Galapagos: Evolutionary solver plugin for GH. 
 Goes through solutions for the Grasshopper.
DIVA: Daylighting and energy modeling plug-in. 
 The Grasshopper’s energy advisor
Karamba3D: Finite Element program fully embedded in GH. 
 The Grasshopper’s structural advisor.
In the following chapter the principles of parametric design will be tried 
out and explained by implementing these methods on an, at the time being, 
ongoing competition project together with Henning Larsen Architects. The 
case is meant to shed light on the possibilities of interactive analysis and 
optimization of a facade, using parametric design.
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CASE [0]
page 25
[European Patent Office - New main office] [Hague]
Rhino Grasshopper Python Galapagos DIVA
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2 | Case [0]: EPO
2.1 European Patent Office - Introduction
2.1.1 About the case
The European patent office in Rijswijk - the Hague, is building a new main of-
fice. The competition team is Henning Larsen Architects and Arup.
At the time of the work carried on this case, the project is in its 2. phase 
and a new and more innovative approach is asked for. The European patent 
office stands for innovation and new inventions as well as looking backwards 
in history. Therefore they want this to be noticeable in their new main office. 
The people working at the European patent office are working very individu-
ally and needs to be very focused on their assignments, as well as doing very 
thorough research. Therefore a proposal of individual cell offices is chosen. 
These offices are where the employees can focus in quiet. Then they can meet 
up with their colleagues in open interactive common spaces. 
As these cells take up the majority of the collected office area and of the 
facade, these are of main interest in the energy optimization. Some of the 
important keynotes for the project are: 
 - Maximum individual user comfort.
 High individual control of comfort.
 High degree of concentrated work with great views. 
 - Optimal functionality.
 Flexibility in the use of spaces.
 Quiet work-space vs. interactive areas.
 Strong central interactive connection areas between departments.
 - Optimal design development and implementation. 
 Future proof design solutions.
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Fig. 2 Main concept. Henning Larsen Architects ©
Fig. 1 New main office - Birdview. Henning Larsen Architects ©
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2.2 Parametric facade design. 
2.2.1 Math surface
An idea of individual working cells within a bigger organism was the driving 
force for the proposals. The important aspects of the facade is to be energy 
efficient in terms of solar shading, natural daylight, glare, air quality, heating 
and cooling for the individual cell workspaces. 
To introduce the method of parametric design, the following example uses 
an algebraic surface as an attractor for the solar shading. In this case the 
idea was that the variation of the surface could enable self-shading and an 
interesting expression. Here the algebraic surface called a “monkey-saddle-
surface” is chosen. This has the algebraic equation:
To create shading, relating to the saddle surface, a point-grid is set up on 
the surface for each cell office. The x- and y-values of each point in the 
planar grid is extracted. From these the corresponding z-value is calculated. 
In this case the operation is done in the xz-plane, meaning it is the y-value 
that is calculated. The rectangular edge of each cell on the planar surface is 
then extruded towards the algebraic surface.
2.2.2 Variations
Parameters in this script are variables multiplied with the x- and z-values, 
the interval of the representation of the surface and a damping coefficient. 
The sliders in the script represents these variations and every change can 
be seen in the Rhino viewport - see Fig. 3. 
For each solution an evaluation can be carried out. To make an example, here 
the material usage is extracted. In an Excel spreadsheet, a specific solution 
to an equation can be found by use of the goal seek utility. A similar tool is 
the extension Galapagos Evolutionary Solver for Grasshopper.
 
x(u,v) = u 
y(u,v) = v 
z(u,v) = u3-3*u*v2 
 
 
z=x(x2-3y2) 
 
 
 
 
 
 
 
Fig. 3 Rhino Viewport
Fig. 4 Sketches
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Fig. 6 Render
Fig. 5 Grasshopper definition. 
The script is set up to input the variables of the surface as input to the 
solver . These inputs are called genomes. Then a “good enough” value or 
fitness-value is defined in order for the solver to be able to find a solution. 
The solver basically choses a combination of genomes within a certain range 
and determines if this combination is good or bad. There is a lot of theory 
behind the evolutionary problem solving and a lot more to explain about 
Galapagos, but it will not be explained in detail here. For more info see: 
http://www.grasshopper3d.com/group/galapagos
The important thing to know, is that Galapagos enables automation of the 
evaluation and optimization process. In this example the surface variables 
are the genomes, and the goal is to fulfil the fitness function best possibly, 
within a chosen interval of the variables.
Next step is to define a good fitness value defining the actual goal. In this 
case the goal is the minimum amount of material and the minimum of solar 
gain. A numerical value of minimum solar gain is simplified to being the minimum 
area of solar radiation for optimization.
Using this method on the design chosen by the architects, is shown in the 
following. 
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2.3 Optimization
2.3.1 What is optimization?
Optimization is the selection of the best solution. Selection with regard to 
some criteria from some set of available alternatives. In the case of para-
metric design it is all about setting up the script so that it matches the 
idea and allows for the necessary variations. Especially for geometry, this 
means setting up a logic for interaction and interconnection of points, lines 
and surfaces. 
The chosen design for the shading is a irregular cassette (Fig. 8). So here 
the exercise is to look at best variations of the corners in terms of maximum 
shading and material consumption.
It is clear that the best solution for minimum material usage is the smallest 
cassette possible. At the same time one of the most efficient solutions to 
minimum solar gain is obtained by a maximum amount of shading or cassette 
size. The graph below shows the obvious - as the size of the casette in-
creases, material usage increase and solar gain decrease.
However there are solutions with different amounts materials, that gives a 
similar result in solar gain. So a defined fitness value is needed to use the 
Galapagos solver and this is possibly the most important part of using an 
evolutionary solver. 
Fig. 7 Materials / solargain relationship
Case [0]: EPO
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2.3.2 Fitness functions
Darwin’s Theory of Evolution states survival of the fittest. But it can be 
very difficult to say what it means to be fit. In evolutionary computation, 
however, fitness is a much easier concept. It can be what ever it is wanted to 
be, because we are trying to solve a specific problem. Therefor we know what 
it means to be fit. The designer needs to figure out which parameters and 
goals are the most important ones. Lets try and set up the fitness function 
in this case. The material consumption is named A and the solar radiation B. 
The distance from the outer corners to the corresponding inner points is set 
to an interval of {1 -> 1000}mm. The interval starts at 1 for computational 
reasons. Firstly the best and worst possible fitness values for A and B is 
set up. This is calculated by using the script and gives:
In table form:
The fitness function: for minimizing both parameters is: 
The above function just states that we want to minimize A and B. Now it 
needs to be normalized, meaning only having values from 0 to 1, and to be-
weighted considering the range.* Then this gives:
The value of this fitness function is for an extended version of the cassette 
shown here (see Fig. 10 on page 33), by adding an extra variable point in 
the centre.
* http://www.grasshopper3d.com/forum/topics/galapagos-multiple-fitness
Fig. 8 Cassette principle
A= matCons. 
B= radArea 
Best fitness: {A=4, B=86} 
Worst fitness: {A=4202, B=4667} 
A {min=4; max=4202; range=4198; target=4} 
B {min=86; max=4667; range=4581; target=86} 
f=-A -B 
f=-((A-4) / 4198) - ((B-86) / 4581) 
A= matCons. 
B= radArea 
Best fitness: {A=4, B=86} 
Worst fitness: {A=4202, B=4667} 
A {min=4; max=4202; range=4198; target=4} 
B {min=86; max=4667; range=4581; target=86} 
f=-A -B 
f=-((A-4) / 4198) - ((B-86) / 4581) 
A= matCons. 
B= radArea 
Best fitness: {A=4, B=86} 
Worst fitness: {A=4202, B=4667} 
A {min=4; max=4202; range=4198; target=4} 
B {min=86; max=4667; range=4581; target=86} 
f=-A -B 
f=-((A-4) / 4198) - ((B-86) / 4581) 
A= matCons. 
B= radArea 
Best fitness: {A=4, B=86} 
Worst fitness: {A=4202, B=4667} 
A {min=4; max=4202; range=4198; target=4} 
B {min=86; max=4667; range=4581; target=86} 
f=-A -B 
f=-((A-4) / 4198) - ((B-86) / 4581) 
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The definition is build up in two parts. The calculation of the sun position 
(cyan) and the generation of geometry (magenta).
The sun calculation part, calculates the sun position at a specific time at a 
specific location and is based on a slightly refined version of a definition by 
Ted Ngai Jan and his visual basic script (VB). This script is build upon the 
solar position algorithm by NOAA*.
The second part is where the shading geometry is created and the radiated 
area is calculated. The engine of this part is the Python script** which turns 
the facade in to an intelligent system. In this system each cell knows about 
its facade mesh, normal vector, inner and outervertices, geometry of the fins 
and it runs the radiation calculation internally. 
The output of this script is the fin geometry and the radiated area as line 
geometry, for faster computation speed. This can then be visualized as solid 
geometry and the area data is used for optimization using the fitness func-
tion mentioned in 2.3.2. 
The variable distances (grey) for the outer vertices become the genomes for 
the Galapagos Solver and the fitness function is used for the to look for 
the best combination. 
The definition can of course be used without Galapagos. Instead of letting the 
solver go through all combinations, one can set up different extremes and 
in between values. These can be evaluated in terms of aesthetics and per-
formance to give an impression of the direction to take. This more “manual” 
evaluation has the advantage of control and speed, but one might very easily 
miss the most optimal combinations. 
* National Oceanic and Atmospheric Administration - U.S. Government
** See appendix A
2.4 Scripting
2.4.1 Grasshopper definition
Case [0]: EPO
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north
12:00
sunrise
sunset
Fig. 9 Grasshopper definition.
Fig. 10 Rhino viewport.
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2.5 Parametric studies
2.5.1 Script calculation - example
This way of systematic modelling with an intelligent system behind, allows the 
designer to evaluate aesthetics and performance at the same time and get 
an idea of in which direction to move forwards. In this case the performance 
output is material consumption, radiated area and the relation between the 
two. 
Studies like these are a good way of gaining common ground for collaboration 
between architects, engineers and other consultants. One the right hand side 
is an example of an evaluation schedule for discussion. Having numbers on the 
performance, while studying design solutions, enables designers and engineers 
to decide whether something is better than something else - both in terms of 
aesthetics and performance. From here they can move on together. 
A similar manual method is common practice at Henning Larsen Architects. In 
such a practice, a model is normally build in a modelling program to visualize 
and it is then transferred or rebuild in an analysis program. The difference 
is the speed and precision that comes with the parametric modelling. The fol-
lowing will show how linking software enhances this procedure. 
sun 5 ,63 m2 
mater ia l 3141 m2 
rel . 0 ,98 
Fig. 11 Evaluation step - example.
Case [0]: EPO
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Summer solstice, 21st June
10 AM
12 AM
14 AM
10 AM
12 AM
14 AM
Equinox, 31st March
EUROPEAN PATENT OFFICE
Parametric optimization of facade structure
sun 5 ,57 m2 
mater ia l 3070 m2 
sun 5 ,29 m2 
mater ia l 2800 m2 
rel . 1 ,041 
rel . 1 ,025
sun 5 ,63 m2 
mater ia l 3141 m2 
rel . 0 ,98 
sun 10 m2 
sun 0 .66 m2 
sun 5 m2 
mater ia l 1 ,2 m2 
mater ia l 16 ,6 m2 
mater ia l 10 m2 
rel . 0 ,06 
rel . 13 , 1
rel . 1
Fig. 12 Example of schedule
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2.5.2 DIVA Analysis
As mentioned in part 1.3.3, the open platform of Rhino3d and Grasshopper, as 
well as the increasing interest in the software, seems to make it an interest-
ing place for software developers. There is many different kinds of plugins 
that will extend the abilities of Grasshopper. Some plugins work with an in-
ternal calculation engine, meaning that everything is done within Grasshopper 
and Rhino. Other plugins acts as a translator between external software. 
These plugins work like adding specialist tools to the toolbox. 
DIVA-for-Rhino is a daylightning and energy modelling plug-in, initially for 
Rhino. DIVA-for-Grasshopper plugin extends these tools to Grasshopper. In-
stead of having the script doing simple geometric calculations of the radiation 
area, this software extension allows for much more advanced analysis. DIVA 
links validated simulation engines like Radiance, Daysim and Energy+.*
In this case it was important to find a shading configuration that allowed 
enough natural daylight into the room, while minimizing the solar radiation on 
the glass, in order to minimize overheating. 
That means that an algorithm that optimise the geometry, in relation to both 
the daylight factor and the solar radiation, is needed. To do this a single cell 
office is modelled in Rhino and the parametric shading is created in Grasshop-
per through the same custom Python script as before. This time the calcula-
tion code is taken out of the script, so that it only creates the geometry. 
The dynamic shading geometry is then analysed in e.g. Radiance, through DIVA. 
DIVA uses the analysis engine of, but does not open, these programs and 
gives fast feedback. Depending on the numerical goal, the fitness function 
is defined and using the Galapagos solver, the best solutions can be found. 
* See www.diva4rhino.com for documentation
Case [0]: EPO
Fig. 13 DIVA data output.
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Fig. 14 GH Def. DIVA + Geometry script
Fig. 15 VIsual representation of daylight factor and radiation on window.
See animation on www.vimeo.com/rasmusholst
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Case [0]: EPO
2.6 Discussion
As a part of the research area of this thesis, a discussion of how far to 
take the written code is interesting. 
Here the Python script for the geometry was setup in collaboration with the 
competition architects. This script divides the facade into the individual cell 
offices and creates a parametric geometry of the solar shading as explained 
previously. 
Then two different approaches was used:
(1) Calculation of radiated area and material usage inside the script
(2) Link to external analysis software through DIVA
The first approach (1) has the advantages of simplicity and interaction speed. 
This means that each iteration is executed fast and therefor can be executed 
in higher numbers - e.g. on the whole facade at once. This can be an advan-
tage as the aesthetics of the facade can be evaluated while going through 
the optimization. 
But at the other hand this simplicity means that only the direct sun on the 
facade is taken into account. The link with external software (Radicance, 
Energy+ etc.) makes it possible to see all the effects of each iteration step 
- this being solar irradiation, illuminance, daylight factor, thermal performance 
etc., but these more detailed processes takes longer to simulate. Here ap-
proximate 10 seconds pr. change
It is clear that in order to be able have full control in approach (2), the de-
signer needs to know about the software that DIVA links to. It is necessary 
to know the setup of the models in order to understand the output that 
comes back into Grasshopper. 
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Fig. 16 Scripting only. Rhino + Grasshopper screenshot
Fig. 17 Script linked with DIVA engine. Rhino + Grasshopper screenshot 
EPO | SCRIPTING
EPO | SCRIPTING + DIVA
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The geometry here was relatively simple and the focus was on energy con-
cerns. It is not hard to imagine doing the modelling and the analysis manually. 
In cases of more complex geometry, the strength of intelligent systems and 
parametric design would come to show. The idea of individual cells within a 
working organism was the driving force for these other proposals: 
2.6.1 Origami cell
Origami is folding of a single element into smaller individual compartments. 
This principle has the properties of using planar and relatively simple ele-
ments as well as having an interesting spatial expression. The idea is to 
somehow figure out and list the building DNA and map the needs of each part 
by the folding origami structure. Meaning that needs for solitary confinement, 
shading, views, acoustics and so on are accounted for by the size,direction, 
angles etc. in each origami compartment. (Fig. 18)
2.6.2 Voronoi cell
When thinking about cells from a mathematical point of view, the Voronoi 
diagram is the first thing that comes to mind. The Voronoi principle can be 
used in two or three dimensions, and can be applied in one or more layers. 
As for the origami principle, the distribution of Voronoi cells accommodate 
for the needs of each individual office. Some cells might spread across of-
fices because of similar needs or external impacts. Especially when adding a 
third dimension and thereby different angles out of the plane of the facades, 
this principle becomes really interesting in terms of structural and shading 
optimization. (Fig. 19)
2.6.3 Karamba3d - Finite Element Analysis.
As the geometry becomes more complex, alternative analysis tools are nec-
essary. DIVA proved handy for energy analysis. When it comes to structural 
analysis, plugin Karamba3d, provides the same kind of flow as DIVA. Here 
tested on a parametric freeform truss. (Fig. 20)
Case [0]: EPO
2.7 Perspective
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CELL | ORIGAMI FOLDING
CELL | VORONOI_math
FREEFORM | TRUSS_analysis
Fig. 18 Initial sketches and references.
Fig. 19 Initial sketches and references.
Fig. 20 GH definition + Karamba. Freefom truss example (RH).
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Using the parametric model and analysis tools, enables teams to optimise the 
shading design dynamically. Together with the Galapagos solver the process 
can be automated. This means that the designer or engineer can work on 
other things, while the computer solves the algorithms set up. So on top of 
saving a lot of time on drawing, redrawing, evaluating and starting over, it 
can be done automatically and perfectly precise. 
This immense increase in speed allows going through large number of itera-
tions - which is the strength of the computer - and see some results that 
might else have been missed. 
Case [0] serves as an introduction and an example of parametric design in 
architecture projects. 
Case [0]: EPO
2.8 Part conclusion
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Fig. 21 New main office - Collaborative zone. Henning Larsen Architects © 
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INITIAL RESEARCH
page 45
[Construction principles] + [Overview] + [Inspiration]
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3 | Initial Research
3.1 Simple advanced structures
3.1.1 Introduction
The strength of parametric modelling and scripting is the complete control 
over all aspects in the modelling. All inputs, outputs and constraints are ac-
cessible. 
This control can be used to create complex systems, where constraints might 
be size of elements, connections, material strengths and so on. These are 
very rational things. Things that are meant to bridge the gap between draw-
ing and building. In the book “Translations from Drawing to Building”* - Robin 
Evans talks about great inventions happening in this very gap. 
When a simple logic is combined with other simple logics, is twisted slightly or 
something similar, unexpected consequences might arise. This makes it pos-
sible to narrow and explore the cap, at the same time. Instead of defining a 
method to execute a project, the method ends up defining the project. This is 
a way of manipulating the tectonic method to define the design. 
Set up correctly, construction information can be generated directly from the 
design information. Rather than having to figure out how to manufacture some 
complex shapes, it is already held within the design. 
Seemingly chaos can be nothing more than simple logics put into system. It 
is structures like these that will be explored in this chapter. It has been 
tried to define categories and to explain these in short, even though some 
principles will consist of overlapping tectonics, such that they might be put 
into more than one category. 
At the end of this chapter, one of these principles will be chosen for further 
investigation and exploration. 
* Translations from Drawing to Building and Other Essays - Robin Evans. (1997)
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system logic
connection
examples
Se
ct
io
ni
ng
Any 3D geometry can be constructed from planar elements by 
slicing through the geometry in two or more directions. 
Normally the geometry is sliced in two orthogonal directions 
and a grillage structure is created. This means that the ele-
ments edges will have to be cut along the curvature of the 
geometry. 
A series of profiles are intersected and connected. This prin-
ciple is known from air plane building and shipbuilding. The 
profiles acts as the structural ribs and can be clad after as-
sembly. 
model
Sectioning
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references
4
2
3
1
1
2
3
4
Fig. 1 Indigo Deli. Sameep Padora & associates.
Fig. 2 Serpentine Pavilion 2005. Siza, Moura & Balmond.
Fig. 3 Metropol Parasol, Sevilla. Jürgen Mayer-Hermann.
Fig. 4 Olympic stadion Beijing. Herzog & de Meuron.
page 50
Folding turns a flat surface into a 3-dimensional structure. 
When folds are introduced into otherwise planar elements, 
those elements gain stiffness and rigidity. They increase 
their span distance and can often be self-supporting. 
The logic is that by introducing curves or lines on one or 
more planar sheets of material and rotating around these 
curves, a new 3-dimensional structure and thereby new 
spaces are generated.
Folding is the further consequence of bending. In materi-
als that allow plastic behaviour, the folding can plastic 
deformation of the material. Folding concepts can be used 
together with those of tessellation. Meaning that the folds 
are rather cuts and connections, in materials too brittle, for 
complete folding. 
Gregory Epps and ROBOFOLD uses Grasshopper + plugins to 
generate and simulate curved folding behaviour. While non-
curved folding is much simpler to simulate. 
system logic
connection
model
Fo
ld
in
g
Folding
examples
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Fig. 5 Richard Sweeney - Paper sculpture
Fig. 6 Andrea Russo - Origami tessellation
Fig. 7 Juergen Weiss - Barcelona Block
Fig. 8 rvtr - Resonant chamber. 
Fig. 9 Ryuichi Ashizawa Architects - Folded Plate Hut
1
3
4 5
references
1
2
3
4
5 
2
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system logic
connection
model
Shells
Sh
el
ls
A shell structure is a spatial structure that is economical 
in terms of materials if designed correctly. The curved shell 
surface geometry can be made out of one or more curved 
elements, in concrete for example, like the structures of 
Heinz Izler and Felix Candela.
However the production of such elements are expensive and 
time consuming. The shell can also be divided into facets 
of planar elements. These facets can be modified to create 
certain properties in terms of light, structure, aesthetics 
etc. 
This division of the shell into planar elements without cap 
or overlap is also called tesselation. This tesselation can be 
divided into layers. Meaning that each division can be futher 
divisioned and modified in or out the original division plane. 
examples
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references
Fig. 10 Roskilde dome - Tejlgaard + Almegaard
Fig. 11 Roskilde dome - Tejlgaard + Almegaard
Fig. 12 BOWOSS Bionic Pavilion - Saarland University
Fig. 13 ICD/ITKE Research Pavilion 2011
1
2
3
4
1
2
3 4
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Bending or flexure ismovement out of one or more planes 
of a planar element. Bending occurs when applying external 
loads perpendicular to an element or in the longitudinal di-
rection of the element. It also occurs from temperature and 
humidity differences. In engineering bending is referred to in 
3 axis - bending of rods is 1-axis, for beams it is 2-axis and 
plates and shells it is 3-axis. If in beams we have “bending” 
around the longitudinal axis, we refer to this as torsion or 
twisting. 
To utilize bending of slender elements, an external load is 
applied and the elements are held in the deformed state 
by fixation. Elements can either be fixed to a predefined 
form work or in systems where internal relations create 
the bending. 
Otherwise non-rigid elements gain stiffness and structural 
stability by this deformation through bending - similarly to 
the description from folding. This can occur in the element 
locally and therefor it become even more significant in net-
works. 
Gridshells are probably the most known structure where 
bending is utilized for an optimised structure. 
system logic
connection
model
Be
nd
in
g
Bending
Twisting
examples
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1
2
3
references
5
4
Fig. 14 Hermes Boutique - RDAI
Fig. 15 Digital Weave - IwamotoScoot
Fig. 19 Timber Fabric - IBOIS 
Fig. 16 Stripmodel test
Fig. 17 Eclaireur Paris - Arne Quinze
Fig. 18 ICD/ITKE research pavilion 2010
1
2
3
4
5
6
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system logic
connection
model
Network
All structures work in some kind of network. Most of them 
are in practical systemized order. This order is of course 
to ease the drawing and building process. Such systems or 
networks are often orthogonal linear systems, as grids for 
example. 
The simplicity of these linear systems can be very at-
tractive aesthetically. Nonetheless, chaotic and seemingly 
random structures has an intriguing appearance. Examples 
of such structures in nature are nests and beaver dams. 
The structural stability is created by interlocking of the 
elements. 
In architecture the interlocking is not restricted to the 
elements themselves, as the systems can be modelled with 
mechanical connections where ever. 
There are two main approaches: 1 - Elements, connections, 
logics etc. define the shape more or less randomly. 2 
- Attraction of an element network towards a predefined 
surface defines the shape.
Logic and algorithm needs to ensure structural stability. 
Rules might be: Each element needs to connect to at least 
two other elements, but not more than four. At least two 
of each connecting elements need to connect in a way that 
ensures triangles. All connecting elements need to be touch-
ing in the same plane, but not intersecting. Many more and 
other rules might be necessary. Here an iterative process 
using Galapagos might be useful. 
Ne
tw
or
k
examples
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“There Is No Chaos 
Only Structure” 
 
- Arne Quinze (2011).
references
1
2 3
4
Fig. 20 Uchronia - Arne Quinze
Fig. 21 Roof installation - Arne Quinze
Fig. 22 CityScape - Arne Quinze
Fig. 23 Aggreation Anenom - Dave Vu and David Pigram
1
2
3
4
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system logic
model
Modules
Aggregates
An aggregate is a collection of items that are gathered to 
form a total quantity. Most structures are made of a num-
ber of elements. In most planar steel structures, beam and 
column elements are used to create a skeleton. In concrete 
structures, often precast modules in practical size are used. 
Somewhat related to the network system, it is important 
that the internal relations between adjacent modules. These 
need to have a common side, edge or some something else 
to connect them. 
It is this relation, the shape of each aggregate and poten-
tially the transformation of these, that creates the overall 
shape and properties of the structure. This is what we now 
from many structures in nature - the backbone for instance. 
Each aggregate can be a module with individual properties, 
other than the structural. This might be light and thermal 
properties. Similarly to a window in a facade, each aggre-
gate can be more less dynamic and respond to surrounding 
impacts. 
Fractals are a similar phenomenon, known from both nature 
and maths. Like aggregate structures, fractals show a re-
peating, self-similar structure.
Mo
du
le
s
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references
Fig. 24 In-Out Curtain - IvamotoScott
Fig. 25 Paper Art - Richard Sweeney
Fig. 26 Voussoir Cloud - IvamotoScott
Fig. 27 Harpa Concert Hall - Henning Larsen Architects
1
2
3
4
5
6
1
6
3
4 5
6
2
Fig. 28 Bent Wood Exoskeletons - .Joel Letkemann
Fig. 29 Differentiated Wood Lattice Shell -Huang + Park
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system logic
connection
model
Gridshell
Gridshells are the most known construction where the bend-
ing nature of wooden elements are utilized for an optimised 
structure. The gridshell structure derives its strength from 
its double curvature, in the same way that a fabric struc-
ture derives strength from double curvature, but is con-
structed of a grid or a lattice.
Large span timber gridshells are commonly constructed by 
laying the laths on top of a sizeable temporary scaffolding 
in the wanted shape, which were removed in phases to let 
the laths settle into the desired curvature. A recent project 
example is the Savill Garden gridshell
Another approach is initially laying out the main lath mem-
bers flat in a regular square or rectangular lattice, and 
subsequently deforming this into the desired doubly curved 
form. This can be achieved by imagining to push the members 
up from the ground. Similar approach is used in the Mannheim 
Multihalle. Here Frei Otto used hanging models.
Two different approaches are:
1. From wanted shape to grid and connections. 
2. From planar grid to shape by moving of constraints.
Gridshells might be made out of any elastic material, but is 
mostly made out of wood. The material properties, joints, 
grid and constraints are defining factors for the shape. 
Members need to be slender enough to bend, so in some cas-
es, the structure has to be constructed in multiple layers. 
Gr
id
sh
el
l
examples
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references
Fig. 30 Centre Pompidou, Metz - Shigeru Ban + Arup
Fig. 31 The Savill Gardens - Glen Howells Architects
Fig. 32 Centre Pompidou, Metz - Shigeru Ban + Arup
Fig. 33 Gridshell Digital Tectonics - Smart Geometry ‘12
Fig. 34 Centre Pompidou, Metz - Shigeru Ban + Arup
1
2
3
4
5
2
4
1
3
5
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Research
3.1.2 Part conclusion
Many of the structural principles overlap in the catergorization. Many of 
these are closely related and combinations of them hold very interesting 
potentials. For instance combining bending + modules + network. Some of 
the referenced elements in the module part can be bend plate elements and 
worked in a more or less complicated network. 
Gridshells are mostly considered to construct a single three dimensional 
surface and sometimes offsets of this surface. A combination with principles 
from the more multidimensional network part, could prove to be an interesting 
kind of weave structure. Here elements can move in and out of the surface 
and start and end wherever, on or off the surface. 
The common thing for the presented structures are that they are different. 
Different from what is normally built and advanced in the looks of it, but 
pretty simple in the logic. Most of them are impossible or at least very time 
consuming to create without computationand scripting. 
Most examples are built as study-cases, casual pavilions, installations or 
furniture. The transformation from these principles to building elements, wall, 
floors, roofs etc. are very challenging, but also very exciting. It is tempting 
to put the conventional thought to the back for a while and think of buildings 
as multidimensional structures - not necessarily divided into floors, walls and 
roofs, but as a coherent environment. 
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3
Fig. 35 Tripudio Bestia - Matthias Pliessnig Fig. 39 Lamella flock - CITA
Fig. 36 Allotropic System - Nicholas Bruscia Fig. 40 Plasti(K) Pavilion - Marc Fornes THEVERYMANY
Fig. 37 Centre Pompidou, Metz - Shigeru Ban + Arup Fig. 41 Dorian Pattern Facade - Khiem Nguyen
Fig. 38 Resoloom - Peter Vikar Fig. 42 Migration - Matthias Pliessnig 
page 64
3.2 Gridshells
From the initial research, the gridshell structure is chosen for further in-
vestigation. The reason for choosing this principles is the direct utilization 
of bending in networks of slim regular elements. The thought is that when 
knowing how to construct more regular lattice gridshells, it is possible to 
combine this with some of the more random looking structures from the net-
work part. This combination might end up somewhat like the pictures on the 
right hand side. 
The further investigation approach will look into parametric tools for form 
finding and the simuation of element behaviour. The first step is to setup 
an intelligent system that resembles the properties and geometry of real 
elements. 
Afterwards the elements will be put into networks, such as the lattice in 
the gridshell. Constraints in relation to connections and supports will be in-
vestigated. 
A really important part of setting up such a system, is the ability to evaluate 
in terms of curvature, stresses, moment distribution etc. and in the end be 
able to translate the model to building elements. 
The prospects are that such a working method will enable the construction 
and analysis of complex geometry surfaces for whole building envelopes, roof, 
facades interiors etc. At the same time the thesis is that by setting up this 
scripting system, one will be able to create optimised structures, using similar 
approach as mentioned in chapter "2.3 Optimization" on page 30.
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Fig. 43 Hello wood
Fig. 44 Eclaireur Paris - Arne Quinze
page 66
MODELLING
page 67
[Interactive physics]
Rhino Grasshopper Python Kangaroo
page 68
4.1 Paper play
4.1.1 Physical investigation.
Physical models are used for investigation in order to setup the 
needed script. By simple physical studies of shapes created by defor-
mation, an idea of the behaviour is obtained. In the case of gridshells, 
it is interesting to look at what effect the initial grid has on the 
behaviour of the deformation and stability. 
Investigations include the shapes that is created from changing fix-
ing points of the planar grid, the significance of connections and the 
deformation of individual elements. 
Another approach of the investigations is to lay a grid of strips on 
a already defined/built surface, fixing these at intersections on the 
surface and thereby finding the necessary grid configuration. The 
grid created by this method, is not necessarily planar. It is a way of 
constructing a predefined shape. This is particularly interesting for 
architectural projects in search of a certain shape..
When laying and interlocking strips on top of a surface, the relation-
ship between element connections, material flexibility etc., creates 
3-dimensional structure. This interesting effect that will be investi-
gated later on. 
4 | Modelling
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Fig. 1 paperPLay - first physical test with regular paper. From grid to form.
Fig. 2 paperPLay - First test: From form to grid.
page 70
4.2 Theory
Modelling
4.2.1 Compression members
To create the deformations of the paper model, the members are subjected 
to external forces. The basic theory of this behaviour is that of compression 
members. 
A compression member - or a column - can be defined as a beam subjected to 
a compression force acting in the beam axis (local x-direction). Basically the 
theory can be divided into short columns and long columns. Short columns 
has the property that a column of the same cross section has the same load 
carrying capacity. If subjected to a bending moment, by e.g. eccentric loading, 
the stresses are found by Navier’s equation: 
Long columns or slender columns are characterized by being forced to de-
flect when subjected to a sufficiently large normal force. If a simple linear 
elastic member is subjected to normal force N, that gives the deflection 
u(x). Moment equilibrium at any given point x is:
For a member of linear elastic material with small deflections:
Curvature κ can be defined as:
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
(1)
(2)
(3)
(4)
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page 71
Which then gives the relation between moment and curvature:
Local curvature of a spline geometry can also be found geometrically by:
where R is the curvature radius. 
Equations (5) and (6) means that bending moment can be found by:
Stresses can then be found by either:
or by Navier (1):
At the same time the critical Euler load can be found by putting (2) and (3) 
together:
and rewriting this as a second order differential equation:
Solving this gives:
The critical load might be used to determine what force is needed for any 
deformation. This theory will be used later to find stresses, forces and mo-
ments in the bend members. 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
NA
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
Normal stresses : σc=
N
A
 
Moment stresses : σm=±
M
W
 
Combined stresses : σt= NA - MW σc= NA + MW 
 
M(x)=N*u(x) 
M(x)=-EI* d2u(x)
dx2
 
d2u(x)
dx2
=-κ 
⇒κ=-
M(x)
EI
 
κ=
1
R
 
M(x)=κ*EI 
M(x)= 1
R
*EI 
σ = E*ε = -yEκ 
σm=±
M
W
 
 
 
EI*
d2u(x)
dx2
+N*u(x)=0 
k2=
N
EI
 
⇒
d2u(x)
dx2
+k2*u(x)=0 
⇒Nel= π2*EIls2 
or
page 72
4.3 Physical modelling
4.3.1 Particle system
The digital modelling will be carried out using add-on Kangaroo. It allows the 
user to interact in real time with the model as the simulation is running. The 
Kangaroo engine is based on relaxation of a particle system. 
Particles are points or objects in a system that can have mass, position and 
velocity. They respond to forces, but have no spatial extent. Despite their 
simplicity, these particle systems can be set up to exhibit a wide range of 
physical behaviours. A system built by connecting particles with simple damped 
springs can resemble a wide variety of nonrigid structures.
“Macroscopic properties of materials such as the behaviour in bending, 
shear and torsion can actually be seen as emergent* on a molecular level 
from simple interaction between pairs of particles” (Kangaroo Manual)
This means that it is the interaction and behaviour of the millions of parti-
cles/molecules that gives the overall bending behaviour that we know from 
a plate for example. It is clear that the amount of particles in these compu-
tational simulations are vastly smaller than in the real world. With the right 
knowledge, real world behaviour can be translated into the distribution of 
points and springs, as well the internal relations between particle-particle 
and particle-springs. The results can be used for comparison between the 
two. This approach can give a good approximation of the real world physical 
behaviour. 
Even though this particle system has its limitations, it has the advantage of 
being fairly easy to understand and control. The theory behind the system 
just described, will be explained in the following step-by-step. 
* Developing / under development.
Modelling
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4.3.2 Dynamic relaxation
The aim of dynamic relaxation is to find a geometry where all forc-
es in the system is in equilibrium. As mentioned in the introduction 
chapter, the likes of Gaudi and Frei Otto did the dynamic relaxation 
using hanging chains and weights, soap films etc. 
So by discretizing the continuum, meaning dividing an element into 
smaller pieces, the particle system is setup. In the example on Fig. 
3 a steel rod is simulated.
When a force is introduced to the system, an iterative process 
follows by simulating a pseudo-dynamic process in time, with each 
iteration based on an update of the geometry. The basis is to trace 
the motion of each node of a structure, step-by-step for small 
time increments, ∆t. Due to artificial damping, the structure can 
come to rest in static equilibrium. 
The first influence in the system is the desire of each part ele-
ment - spring [si] - to reach its rest lenght. In most materials and 
in this example the rest lenght of [si] is the initial length as the 
material does not want to shrink. 
When particle [p5] is moved to towards left, the spring stiffness 
for [s4] introduces a force vector [v5] acting on particle [p4]. At 
the same time the stiffness of the spring [s3] between [p4] and 
[p3] introduces an opposite reaction force vector [v3] to [p4]. This 
then happens throughout the particle system - [p4] pushes on [p3], 
[p3] -> [p2], [p2] -> [p1] etc. 
To reach equilibrium each particle node moves, so that all vector 
forces acting on it is equal. If [p0] is fixed particles equally divide. 
p0 p1 p2 p3 p4
p4
p4
p4
p3
p5
s0 s1 s2 s3 s4
p5
rest length
v5 v3
v5 v3
p4
v5 v3
Fig. 3 1D dynamic relaxation
Fig. 4 Spring component 
page 74
Previously the system was only introduced to forces acting in line, 
lets call it planar force, this means that there are no out-of-plane 
forces in the system. This needs to be introduced in order to cause 
bending of the rod. This is one of the big differences from the real 
world to the idealized system. 
As soon as an out-of-plane force is introduced to the system, the 
particles move in different directions corresponding to the direction 
of the force vectors introduced. In this example; when moving [p5], 
the stiffness