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A d v a n c e s i n A r c h i t e c t u r a l G e o m e t r y
Vienna, Austria September 13-16, 2008

Geometry lies at the core of the architectural design
process. It is omnipresent, from the initial form-find-
ing stages to the final construction. Modern geomet-
ric computing provides a variety of tools for the effi-
cient design, analysis, and manufacturing of complex
shapes. On the one hand this opens up new horizons
for architecture. On the other hand, the architectural
context also poses new problems to geometry. Around
these problems the research area of architectural ge-
ometry is emerging. It is situated at the border of
applied geometry and architecture.
This symposium brought together researchers from
the fields of architecture and geometry to discuss re-
cent advances in research and practice and to identify
and address the most challenging problems. We con-
nected researchers from architectural practices and
academia. The event consisted of two parts, two days
of hands-on workshops followed by two days of oral
and poster presentations in conference style, featur-
ing prominent invited speakers.

        




      
   

    


    
   
      
     



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Conference Proceedings

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AAG 2008
Advances in Architectural Geometry 2008

First Symposium on Architectural Geometry
Vienna, Austria

September 13-16, 2008

Conference Co-Chairs:

Helmut Pottmann,
Vienna University of Technology

Axel Kilian,
Delft University of Technology

Michael Hofer,
Vienna University of Technology

Co-sponsored by RFR and Waagner-Biro Stahlbau AG

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Complex geometries in Wood

Martin Tamke
Royal Academy of Fine Arts,

School of Architecture

Mette Ramsgard Thomsen
Royal Academy of Fine Arts,

School of Architecture

Jacob Riiber
Royal Academy of Fine Arts,

School of Architecture

Abstract

The versatility of wood constructions and traditional wood joints
for the production of non standard elements was in focus of a
design based research. Herein we established a seamless process
from digital design to fabrication. A first research phase centered
on the development of a robust parametric model and a generic
design language a later explored the possibilities to construct
complex shaped geometries with self registering joints on modern
wood crafting machines. The research was carried out as
collaboration with industrial partners.

Keywords: Digital production, CAD/CAM, Parametric design,
complex form, mass customization, industry cooperation, design
research, Case study

Figure 1: 1:1 prototype showcasing the potential of wood joints
for non standard element architecture

1 Design Research
In his book "The Projective cast" Robin Evans (1995) points out
how the development of techniques changed architecture and the
space inhabited in times of Gothic and early Renaissance. Today a
similar change due to the adoption of computational techniques
into architectural design can be observed. The yields of digital
design techniques are accompanied by a further dissolution of the
link between concept, shape and production, a phenomenon
Michael Speaks (2000) calls the "Dimishing of connection
between form and ideology". Whereas the computation of
geometry proceeds in design on fast pace using relational
geometry the later construction and production does not pick up
digital opportunities to the same extend.

This is remarkable as building industry and the crafts have
invested heavily in digital machinery and processes in order to
increase productivity. But equally to the field of architecture new
techniques resemble primarily the traditional production
processes. Seamless digital workflows between the partners in the
building process could enable the construction of more complex
geometries using non standard elements for the build; this
especially as the machinery in small and midsized craft related
companies bear a high versatility.

2 Wood and joints
Wood is generally considered as one of the most sustainable
building materials. It as well is connected to an enormous range of
different ways of processing and joining. Especially the ability to
easily process the joint directly from the material itself is
remarkable. �The benefits of components with integrated
attachments geometry are that the attachments can be designed
and controlled as part of the generative process� as Larry Sass
(2006) states . Based on a long tradition in the crafts wood-wood
joints, especially those based on friction as dovetail joints, have
advantages:

� Can be specific to certain geometrical and tectonic
requirements

� Monolithic setup allows unrestricted movement

� Inherit tolerance

� High level of prefabrication

� Efficiency in assembly due self registering joints and
little or less secondary elements, as screws or bolts

Precedent research has shown the advantage of implementing self
registering joints that can adapt geometrically to specific local
requirements in the construction (Holzner 1999, Kilian 2003,
Schindler 2007). The required production capacity is given in
modern highly flexible CNC wood joinery machines. They enable
not only the very fast production of individualized wooden beams
but as well the rational production of geometrical complex
individual joints that fit with little tolerances.

Usually material and machining costs are not the main factor in
the fabrication of constructions- labor, production and transport
are at most equally important (Westney 1997). The easy assembly
of elements due to the interplay of high precision and almost total
prefabrication due to CNC manufacturing and the easy assembly
of elements with self registering joints reduce the costs for
complex constructions in wood. Geometrical almost unrestricted
joints should furthermore enable new ways of design.

3 Repetition and Series
As modern techniques allow for mass customization, the focus of
design shifts from the constitution of a solution (i.e. single
elements), that already has the final overall output in terms of

S
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geometry and internal distribution of functions imbedded, towards
the definition of relationships between the elements in play.
Herein the difference between the elements informs a possible
final geometry. As the constitution of every element may varies
the formulated overall geometry is just one out of many � solely
defined by the given parameters and the setup of the internal rules
of interaction, which becomes the main design task . The evolving
systems oriented on a Deleuzian (Keith Ansell-Pearson 1999)
understanding allow new ways to think design. It allows for the
easy exploration of a multitude of design solutions. Herein the
momentum of series becomes a crucial part as it chances for
evolution and adaption to different states. The drawing of
difference within the series can result in gradual as well as sudden
shifts. Yet unlike classical products of mass customization, as first
seen within the work of Artists as Andy Warhol (Collings 1998)
or nowadays in customer products (Reebok 2008), the elements in
our design setup are not solely changing properties but topology.
In addition to the examination of change over time, represented in
the diagrammatic linear alignment as in the mapping of different
states of an object due to movement of its parts, first examined by
Eadweard Muybridge (Clegg 2007) and Étienne-Jules Marey
(1890), we introduced topological change and its infliction with
the designs overall appearance. So the appearance of internal
spaces, poche and openings became a strong moment within our
design exploration.

4 Design Concept
Starting from a real building project � the façade of a large scale
multi storey Parking lot, wherein a parametric concept using CNC
wood manufacturing processes was proposed (Design: Martin
Tamke and Blunck & Morgen Architects Hamburg) � the research
project looked at ways to explore the link between design intent,
formal and special expression and the realization process.

Fig.2: Initial Design Concept: a series of kinked beams create an
overall surface with changing transparencies and patterns. The

diagram shows possible sections through the construction shown
in the rendering on the right.

The basic idea of the design, as shown in fig.2, consisted of evenly
divided but differently kinked beams. Looking at the overall series
appearance wavelike patterns with changing transparencies and
densities appear, when ever the observer moves along the facade.

5 Design of Parametric Model
First investigations of the design showed that it could be easily
transferred into a parametric model based on the structures axis
system. As the concept consisted of only a few determining
parameters it could serve as a well-defined starting point for
further geometrical experimentation. The parametric model itself
consisted of three nested interacting levels with individual sets of
parameters:

� Basic layout of rails and distribution of beams

� Beam structure (represented by mid axis)

� Solid shape

The parametric model not only allowed a direct link to production
in the very first design process due to the embedding of
fabrication specific parameters but as well the exploration of
several variations within the design until certain predefined or
evolving performance parameters were met. These parameters
were later defined by tectonic, material, fabrication and aesthetic
considerations. The exploration was conducted in an iterative
process. Every design iteration led to a physical scale model,
whose constituting elements and emerging nature could be
discussed. These were distilled and emphasized in the next
generation of models. By doing so a individual design language
could be established.

Fig.2: Setup of the parametric system from basic layout of the
guiding rails and axis systems to solid shape representation.

5.1. Interfacing - Control of the system
With a view to an intuitive handling (Burry 2005) the systems
control via diagrammatic representations showed good results
(called law curves in the tools underlying software package
Generative Components). Whereas first models showed a direct
and foreseeable reaction to changes of parameters, later ones with
more and interdependent parameters showed more complex
behavior. This led to the design of an abstract second order
representation of the parameter driving law curves. This deflection
showed good results, counterfeiting the fact that the addressing of
specific areas and phenomena within the model became harder to
predict the more parameters were in play.

Fig.3: Laser cut wood model directly processed from Fig 2
parametric system

5.2. Internal behavior
Being able to address the overall composition and inter-element
behavior of the design as well as the internal properties and
geometrical setup of every element offered a wide range for
manipulation, such as dimension and kink. In the course of the
process further shifts were introduced, i.e. amount of members,
tilt, density, spacing and creasing. Branching led to desired
topological change. Several design iterations proved the
robustness of the chosen parametric model. Yet vast amounts of

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processed and organized coherently, other computational tasks
become easier to handle. Another is that the approach is
procedural, that is, programming-oriented, and this may distract
designers from their initial design activity. Yet, the knowledge and
ability to control modeling procedures and parameters must be
regarded as the foundation by means of which the computational
requirements of subsequent design applications can be addressed.

Acknowledgements

I wish to thank Professor Ramesh Krishnamurti and Professor
Kenji Shimada for their insightful comments and inspirational
discussions. I would also like to thank my colleagues at
Computational Design for their encouragement and support.

References

AKLEMAN, E., SRINIVASAN, V., AND MANDAL, E. 2005.
Remeshing schemes for semi-regular tilings. In Proceedings of the
International Conference on Shape Modeling and Applications,
44–50.

AKLEMAN, E., SRINIVASAN, V., MANDAL, E., CHEN, J.,
MELEK, Z., AND LENDRENEAU, E. 2004. Topmod:
topological mesh modeling system.Tech. rep. Texas A&M
University. Department of Architecture.

CUTLER, B. AND WHITING, E. 2007. Constrained planar
remeshing for architecture. In Proceedings of Graphics Interface,
11–18.

KILIAN, A. 2006. Design Exploration through Bidirectional
Modeling of Constraints. PhD thesis, Massachusetts Institute of
Technology.

LIU, Y., POTTMANN, H., WALLNER, J., YANG, Y.-L., AND
WANG, W. 2006. Geometric modeling with conical meshes and
developable surfaces." ACM Transactions on Graphics 25(3):
681–689.

MOUSTAPHA, H. 2006. Architectural Explorations: A Formal
Representation for the Generation and Transformation of Design
GeometrY. PhD Thesis, Carnegie Mellon University.

MULLER, P., WONKA, P., HAEGLER, S., ULMER, A., AND
Gool, L. 2006. "Procedural modeling of buildings." In
Proceedings of SIGGRAPH 2006, 614–623.

POTTMANN, H., BRELL-COKCAN, S., AND WALLNER, J.
2006. Discrete surfaces for architectural design. In Curves and
Surface Design : Avignon 2006, P. Chenin et al., Eds., 213–234.

POTTMANN, H., LIU, Y., WALLNER, J., AND WANG, W.
2007. "Geometry of multi-layer freeform structures for
architecture." ACM Transactions on Graphics 26(3), Article No.
65.

PRUSINKIEWICZ P., AND Lindenmeyer, A. 1990. The
Algorithmic Beauty of Plants, Spring-Verlag, New York.

STINY G. 2006. Shape: Talking about seeing and doing, MIT
Press, Cambridge.

Page 132

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A d v a n c e s i n A r c h i t e c t u r a l G e o m e t r y
Vienna, Austria September 13-16, 2008

Geometry lies at the core of the architectural design
process. It is omnipresent, from the initial form-find-
ing stages to the final construction. Modern geomet-
ric computing provides a variety of tools for the effi-
cient design, analysis, and manufacturing of complex
shapes. On the one hand this opens up new horizons
for architecture. On the other hand, the architectural
context also poses new problems to geometry. Around
these problems the research area of architectural ge-
ometry is emerging. It is situated at the border of
applied geometry and architecture.
This symposium brought together researchers from
the fields of architecture and geometry to discuss re-
cent advances in research and practice and to identify
and address the most challenging problems. We con-
nected researchers from architectural practices and
academia. The event consisted of two parts, two days
of hands-on workshops followed by two days of oral
and poster presentations in conference style, featur-
ing prominent invited speakers.

        




      
   

    


    
   
      
     
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