GEOMETRIAS’14 PROCEEDINGS - Maio/May 2014 ISBN 978-989-98926-0-6
SESSION 4 - ARCHITECTURE AND GEOMETRY
18 . 05 . 2014
ARCHITECTONICS: 1ST YEAR DESCRIPTIVE GEOMETRY
FOUNDATION COURSE AT THE TU BERLIN
Chr. Barlieb
ABSTRACT
Since the nineteen seventies descriptive geometry was taught to first year architecture students at the
TU Berlin’s Institute of Architecture by drawing with chalk on blackboards and slideshows describing
the construction of various projection methods, as seen in the traditional architecture practice.
Furthermore, there was no link between the descriptive geometry department, the first year design
studios or the CAD department, thus creating a fragmented curriculum. In an earlier paper entitled
Rule Based Design at the TU Berlin, Barlieb et al. [1] explored didactic methods to teach digital parametric design tools. This impetus lead to speculate on conveying digital and analog tools to students,
focusing on describing spatial relationships while aiding pupils to discover and refine their own architectural language, hence “architectonics”.
The following paper tackles the questions: how can we integrate descriptive geometry into the core
curriculum of first year design? How can we introduce theoretical and practical notions of analog and
digital forms of representation to a Facebook generation of students?
The new architectonics lab at the TU Berlin is currently experimenting with these and other related pedagogical issues. Strategies on how we may arrive at hybridizing analog and digital sensibilities in first
year design studios are articulated in the paper. We plan to introduce didactic methods, lectures and
exercises currently employed to train students in the art of decoding and encoding space.
INTRODUCTION
how to integrate the department into the first
year design studios?
Secondly my vision was to create a hybrid form of
pedagogy based on traditional hands-on analog
skills meshed with the contemporary digital era.
My predecessor’s argumentation was: the study of descriptive geometry is mathematical; its
In the Fall 2013 I took on the Chair of Descriptive Geometry at the TU Berlin. Being familiar
with the school, my predecessors and their
pedagogical ideas, I focused my attention on
creating a new dynamic around the question;
Chr.BARLIEB, TU Berlin, Fakultät VI, Sekretariat ACK 19, Ackerstraße 76, 13355 Berlin (c.barlieb@tu-berlin.de)
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purpose is to produce exact representations of
three dimensional (3D) bodies and to solve spatial problems in two dimensions using geometrical means, thereby training the spatial experience necessary to the practice of architecture [2].
While these concepts may be true, I wonder if
they aren’t biased and out of touch with today’s
digital culture? Lynn suggests
The ultimate goal is: to hand down a set of tools to students and teach them to see, or in
other words, how to read architecture, to then
translate it into a new architecture; hence the
ideas of decoding and encoding.
Referring to the seminal texts from our architectural heritage, we discover architects busy
recording and decoding their predecessors:
Vitruvius studied the Greeks, Palladio studied
Vitruvius, Viollet-le-Duc studied the Middle
Ages, etc. Finally, Le Corbusier hit a wall and
found himself at a crossroads between the
Greeks and his contemporary engineering culture of machines. Rem Koolhas was later forced to explore the verticality of architecture, its
compactness and layering. The point is we
are obsessed with learning from the past and
confronted by the present in order to develop
something new. These are some examples of
decoding architecture.
Encoding architecture is just as exciting. For instance: Palladio took his Vitruvian research and
encoded it into what we know as Palladian architecture, Peter Eisenman took Palladio and
made House X; Henri Labrouste’s Bibliothèque
“challenging these assumptions by introducing architecture to models of organization that are not inert will not threaten the
essence of the discipline, but will advance
it, […] an animate approach to architecture will subsume traditional models of statics
into a more advanced system of dynamic
organization” [3].
These notions combined with my experience
working with Prof. Raimund Abraham of Cooper
Union in New York City lead me to question the
pedagogical means of teaching spatial cognition
to freshmen students of architecture.
The outcome to some of these questions is
reported in this paper. It focuses its attention on
teaching students how to decode (to decipher)
and to encode (to convey symbolically) architectures. The paper explores four didactic methods,
lectures, autodidactic study, exercises conveying
digital and analog tools, and using these tools
focus
on
describing
spatial
ced by his contemporary, Viollet-le-Duc’s anthology of medieval and gothic architecture (Dictionnaire raisonné de l’architecture française
du XIème au XVIème).
So when and where have architects learned how
to decode and encode architecture?
While there exists analysis courses taking apart
buildings to understand their programmatic
structures and others search for proportional
systems, it appears few reduce architecture to its
spatial study without delving into diagrams or dry
mathematical theorems.
relationships
own architectural language.
ARCHITECTONICS
Descriptive Geometry (DG) department was to
rename it. I purposefully chose the word “ararchitecture” [4] and since the word “tectonic”
implies structure, it seemed appropriate as I am
researching the semantics of architecture.
A COMMON GROUND
While evaluating the work of Preston Scott
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Cohen, Moneo compellingly reinforces the
notions that
LECTURES
“geometry can be a tool to deconstruct
To communicate these ideas to students, I developed a lecture series reinforcing the culture of
drawing, the visual communication of space and
architecture as demonstrated in the writings and
drawings of the Masters. Unlike my predecessors
that spent their time drawing the mathematical
rules of projective geometry on the chalkboard,
I chose to visually and dynamically explain the
origins, philosophical implications, the tools and
the architectures.
The lecture series meandered through decoding
and encoding, light and shadow, the history of
geometry, indexical and combinatorial techniques, the status quo, perspective from many
perspectives, to name a few. The lectures are
online at our website www.fgbarlieb.de and have
the particularity of pointing the users to highly
detailed digital scans of original facsimile found
in libraries around the world. Being a collector of
original manuscripts, I believe it is important students gain access to digital facsimile of seminal
works to grasp the dedication necessary to producing and revealing architectural space.
memory into another set of ideas and
that projective geometry can transcend
and transform the burdensome questions
of type” [5].
This suggests descriptive or projective geometry
could be used to investigate the semantic qualities of architecture.
I would argue the idea of deconstructing memory
is a key to learning how to decode architecture.
Abraham refers to Heidegger’s “Ort” (a site, a
place, a point) so infinitely small where all forces
and vectors are concentrated and liberated, released as energy, transformed into matter into
built form. Abraham proposes
“the transformation becomes the history of
the site as place, while the cognition of forces
and vectors becomes the memory of events
[…]. The manifestation of the memory of
spatial events from history of the site is idealized through the abstraction of the language
of architecture.”
Abraham’s conclusion is
“architecture
becomes
the
idealized
EXERCISES
language of historical associations whereby
ideal ought to be defined as a form of
The following exercises are a case study put into
practice during the Fall semester of 2013-2014
at the TU Berlin Institute for Architecture (IfA) to
train students in the discipline of architecture
and of applying the training back onto their first
year design studio.
1. Dot Zero: is the first of a series of exercises developed to address the practice of decoding and
encoding space. A Cartesian coordinate composed of the X,Y & Z axes (no larger than 50x50x50
cm, Fig. 1) is designed to be portable and built of
resilient materials by the student. The resulting
precision tool is used to measure and record an
architectonic space.
radical clarity.” [6]
THE DIDACTICS OF ARCHITECTONICS
Learning to encode architecture is a long
process; however it can be accelerated by
remaining in an abstract procedural environment
jumping in and out of imaginary space, physical space and virtual space while confronting
it with practical moments. The three following didactic methods: lectures, exercises
and autodidactic research are used as
foundations which are built upon in the
design studio.
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Fig. 1 - Dot Zero. T. Hemig
2. Recoding Space: A Cartesian coordinate composed of the X,Y & Z axes is used to measure
and record an architectonic space. The student
carefully place the Dot Zero tool in space and record a series of six black and white photographs
along each of the individual axes (+X, -X, +Y, -Y,
+Z, -Z). Black and white photography is chosen to
emphasize the spatial qualities by concentrating
on light and shadow.
3. Tracing (cropping, cartography, codex of
points, lines and planes): The six photographs
are printed on DIN A3 format sheets of paper.
Three sheets of double sided Mylar 28cm2 (Fig.
2) are used to crop the images and focus on generating new compositions. The students are
required to decode their photographs by tracing
key geometries and to develop an architectural
codex of lines (solid, dashed, dotted, dash-dot,
etc). Each Mylar sheet is perceived as a “window
pane” so that one side of the pane is the positive
direction of an axis while the reverse side is the
negative direction of the corresponding axis.
This leads to a disciplined study with pencil, paper, compass and parallel ruler drafting tools, dashed lines are drawn as if sewn by a machine and
line weights and erasing techniques are explored
to highlight the tectonic qualities of drawing.
4. Analog to Digital (scan, points, vectors, lines,
splines and planes): In a subsequent exercise the
drawings are digitally scanned and traced using
vector based drawing tools such as Adobe Illus-
Fig. 2 - Pencil on Mylar. D. Ortner
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bled in virtual space using Grasshopper visual
scripting components. This exercise is the first
time students interact with a powerful parametric design tool. Because the design space is
simple (a point, a vector, a picture plane and a
projection plane) and contains a vast amount of
data, the students rapidly realize its power
and logic.
This visual form of scripting is essential to architects as they are not trained as mathematicians in abstract scripting languages; instead
they demand and require visual spatial cues for
composition. The iterative nature of the environment enables students to rapidly experiment
with variations of their studies and to visualize
them in 3D for the first time (Fig. 3). It is also the
chance to address the concept of the algorithmic in architecture. What’s more is the students
are controlling the tool; the tool is not controlling
the students or their work! The arguments that
digital experimentations can lead to new architectures is a wonderful concept yet I believe they
are more relevant to Master students pursuing
research versus Bachelor students learning the
foundations of the discipline of architecture. This
may shift with the advent of new media or new
spatial cognition theories.
Fig. 3 - Parametric Model. B. Rusch
trator thus focusing on pure vector based software instead of creating confusion by introducing more complex CAD software. Essentially we
are focusing on understand what the difference
is between a vector and a bitmap while promoting the idea that hand drawings can be rapidly
scanned into the computer and traced
accordingly.
5. Project and Control (export, import, algorithm, encoding space): The Illustrator drawings
are then imported into Rhinoceros CAD software using the DWG CAD file format and reassem-
Fig. 4 - Paper Model. S. Schoelhammer
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6. Modeling: The decoded line drawing window
panes are used to encode and build three di-
engineered by students to learn about light projection geometry and shadow drawing techniques.
lines could mean i.e.: cutting, scoring, creasing,
folding, and bending (Fig. 4). The models are purposefully made of paper to address the concepts
Autodidactic research
Descriptive geometry seems like it’s the perfect
autodidactic course. Since I rebuilt the entire department to serve the purpose of decoding and
second semester while building a 1:1 prototype
of one of their models.
students would learn descriptive geometry terms such as: projection, platonic solids, conical
sections, splines, freeform geometry, axonometry would be on their own time, studying in the library so we could spend our studio time learning
how to draw, translate and transform architecture. This turned out to be a success and we’ve
7. Light & Shadow: The models are illuminated in
a photo studio environment to demonstrate composition and exposure of a photo camera picture
plane. The new images are used to gain practical
experience with shadow casting and are reversed
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taken the best redacted works on the various topics and edited them into a book for the students
by the students.
craft space using the architectural vocabularies,
grammars and syntax along with the codex of
points, lines, planes, curves and surfaces.
The meshing of digital and analog tools along
with procedural modes of transformation leads
to and develops abstract and logical forms of
spatial cognition. My goal is to pursue this hybrid
form of creation by promoting the long tradition
of hand crafted architecture while experimenting with new digital media and its possibilities
in making new architecture; even as architecture appears to be leaning towards self-generated
systems, its creation will never be separate from
its media or its generators.
Chr. Barlieb
CONCLUSION: INTEGRATION
INTO FIRST YEAR DESIGN
The aforementioned forms of study relative to
the discipline of architecture are required foundations for first year architecture students. The
design studio is the space to put these notions
into practice. Students begin understanding that
what they draw is architecture, and not a representation of architecture!
In essence we are teaching the students to
ACKNOWLEDGEMENT
I wish to thank my teaching colleagues of FG BARLIEB // Architectonics at the TU Berlin IfA: C.Høgsbro,
K.Müller, M.Seitz, our tutors K.Blömers, N.Schüller, V.Lang and R.Weisgärber and secretary K.Krampe
for their unconditional support and constructive criticism. I am indebted to Prof. Donatella Fioretti for kindly lending me her office and to Prof. Ralf Pasel for trusting and inviting me to teach
at the TU Berlin’s IfA.
REFERENCES
[1] Barlieb, Chr., Pfeiffer, S. Rule Based Design Workshop at the TU Berlin, Design Modelling Symposium, UdK,
2009.
[2] Bonnani, A. Darstellende Geometrie I Ein- und Zweitafelverfahren für Architekten, TU Berlin, 1985.
[3] Lynn, G. Animate Form, Princeton Architectural Press, 1999.
[4] Oxford Dictionaries, Oxford University Press, Retrieved April 16, 2014, from www.oxforddictionaries.com/
definition/english/architectonic
[5] Moneo, R. Geometry and the Mediation of Architectural Conflicts: Comments on the Work of Scott Cohen,
Contested Symmetries the Architecture Writings of Preston Scott Cohen, Princeton Architectural Press, 2001.
[6] Abraham, R. In Anticipation of Architecture / Fragmentary Notes, [Un]Built ed. Groihofer, B. Springer-Verlag/
Wien 1996, 2011.
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