How should |I draw rhythms/?/Collapsing the Tetrahedron

Jules Moloney
Collapsing the Tetrahedron: Architecture with(in) Digital Machines
Keywords: architecture, history, drawing, computing

http://www.chart.ac.uk/chart1999/papers/moloney.html

Projections
For theorist / historian Robin Evans, architecture is inextricably linked to geometry and in particular the technique of projective drawing. As he wryly notes in his earlier Translation from Drawing to Building the actual output of an architect are drawings1. The buildings are translations from these drawings and often this resultant built form is as much constrained by drawing knowledge as by construction technology. His last book The Projective Cast builds on this observation to expose the history of architecture as a series of explicit or implicit references to developments in projective geometry: Piero della Francesca's 'turned heads' is selected as the ultimate virtuoso performance in Renaissance perspective projection 2; the use of traits by Gothic architects pushed the masons craft to gravity defying feats 3; techniques of ruled surfaces borrowed from advances in engineering enabled Le Corbusier to develop and realize Ronchamp, the High Court Building at Chandigarh and the Phillips Pavilion 4. All of these remarkable innovations required developments by mathematicians and exacting drafting technique. Thus, The Projective Cast demonstrates the historical development of Architecture as being limited by the ability to describe form on paper, and hence related to the drafting tools and techniques available at any given period.

Historian as draftsman detective, Evans engages drawing in his own text, culminating in a final diagram of the relationships between the designed object (realized building) and projective geometry. In this diagram "Projection and its analogues" (Fig 1) Evans proposes that all architectural activity - thinking, sketching, building and evaluation - is carried out via, in his words, "projective transactions".



Figure 1: Projection and its analogues, Evans 1995

Within this diagram the idea forms as an internalized 'picture' (9,10), it is explored via the architectural sketch (2,4,6), sold to the client via perspective drawing (5) and realized by orthographic drawings (3). The 'designed object' (8) is but one node within this tetrahedron of projective transactions - the majority of creative activity is spent describing the architectural object via drawing. Evans diagram makes explicit the separation between the creative activity of architects and the end result of these activities - the realized architecture.

Design is action at a distance. Projection fills the gaps; but to arrange the emanations first from drawings to buildings, then from buildings to the experience of the perceiving and moving subject, in such a way as to create in these unstable voids what cannot be displayed in designs - that was where the art lay 5

Evans' thesis is an admirable history of architecture and his diagram a useful summary of architectural activity in which drawings is the dominant activity. While Evans is aware of the closure implicit within such diagrams and proposes it merely as a tool to summarize his thesis, in his words a "a reasonable good rough guide" 6, the particular closure I would like to address is the exclusive preoccupation with drawing as the medium for conceiving and developing architecture: physical models are accommodated within Evans' thesis as intermediate modes which require translation via projective drawing; the observation that since the advent of cinema we have had successive generations whose experience of vision has been dominated by the mobile image is not addressed; the fact that by the early nineties computers were increasingly prevalent in architectural studios does not deserve a mention. As an investigation of the influence of geometry via media it is a history that stops with the advent of photography.

Leaving the question of physical models and cinema for another discussion, the questions addressed in this paper are the implications posed by the adoption of digital media. What changes, if anything, by projecting the digital into Evans' diagram? Could new digital technology address the problem of design as "action at a distance"? Would it be possible to revise Evans' diagram, to close down the distance between representation and building?

A review of developments in architecture and computing unearthed three procedures that to my mind have the potential for such a revision - emergence form, immersive editing and computer aided construction. These procedures are presented here via the following examples: artist William Latham serves to illustrate the use of the computer to produce emergent form; technology developed at the University of Illinois suggests the possibilities of the immersive editing of digital models; while the precedent of Frank Gehry's Bilbao project serves to demonstrate the reality of computer aided construction.

Emergence
William Latham is a British artist who, after observing evolutionary processes in nature, experimented with hand drawn systems as a means to extend his formal vocabulary. Taking large sheets of paper, Latham would draw 'evolutionary trees' in which simple geometry is subject to repeated deformation by the application of a few repeated rules. Latham describes his initial discovery of emergent form and his decision to utilize computers.

Simple as the rules of FormSynth were, they seemed to have a creative power of their own. Even though I created and applied the rules, they produced imaginative forms I had not expected ... Systems can assist an artist to create imaginative forms, and computers are good at applying systems, and very fast at drawing. It seems natural to apply the power and speed of computers to realize the potential of artistic systems and extend the creative power of the artist. 7

Latham collaborated with computer programmer Stephen Todd to develop a sophisticated computer application in which the artist delimits the rules by which form can emerge. The initial 'genes' are random numbers that produce a vast quantity of form. This runs autonomously and form emerges according to parameters determined by the designer. The act of designing is the design of the mathematical functions that describe these parameters.



Figure 2: Mutator

It can be argued that once activated, such codified geometry is outside Evans' diagram. Form starts 'life' as a projection - Latham has either a drawn or mental picture of form that may emerge from the definition of parameters. However, subsequent to this initial picture the generation of form is outside Evans' regime of projective representation. Forms exist as algorithmic description rather than projective geometry. Not for long. Latham quickly asserts control in a process analogous to gardening. Form that is of interest to the artist is used as the seed gene for a second program, 'Mutator'. This program produces nine mutations from the chosen seed gene. The artist then intervenes via a range of functions - Latham describes this editing process as being analogous to gardening.

From the artist's viewpoint, using Mutator is like being a gardener. The gardener breeds, weeds out, destroys and selects forms to steer evolution, replacing survival of the 'fittest' by survival of the most 'aesthetic'. 8

Latham's emergent form is literally 'cultivated' according to subjective editorial procedures. He is a visual artist and while he describes the form as digital sculpture his 'pruning' is based on projected images. We are firmly back within the cyclic procedures of projection and evaluation defined by the Evans. There is though, a rustling of 'life' outside the tetrahedral diagram. Emergent form, prior to being represented by perspective projection for editing, is removed from the regime of projective transaction.

Immersive editing
Editing digital sculpture through the evaluation of perspective pictures suits Latham's ends. His 'pruning' is based on evaluating perspective projections which are satisfactory given the final designed object is a picture. However the evaluation of an architectural proposal requires the ability to intuit space as well as form. Evans demonstrates that the architecture evaluation of form and space has been developed primarily on the basis of drawn orthographic and perspective pictures. For those interested in the spatial aspects of architecture recent advances in computer simulation offer the potential for 'experiential' editing of three-dimensional models. Such developments suggest potential for the architect to edit from the point of view of simulated occupation. The aim would be to approximate the spatial experience of the building during the act of designing by 'inhabiting' digital models.



Figure 3: CAVE, University of Illinois

The most advanced technology available in this field is computer automated virtual environments known by the acronym CAVE. Originally developed at the University of Illinois there are now several throughout the world 9. A CAVE is a physically existing room with high quality stereo graphics projected on the walls and on the floor. Real time images of the virtual model are projected from behind and the participant can interact with the virtual model using input devices such as a pointer or data glove. The visual illusion is augmented by three-dimensional sound that interacts with the simulated movement through space.

In terms of architectural space, critics of attempts at such simulation quite rightly make the point that the sensory experience of real space is a total body experience and that we will never be able to reproduce all the nuances of the experience of actual architecture. 10

However as argued by Alan Bridges 'perfect simulation' is not necessary for virtual environments to be applicable.

... virtual environments should not attempt to model the 'real' world in either increasing detail (like Borges' map makers who drew maps at greater and greater levels of detail until they produced a map that fitted exactly over the real space), but rather recognize that the participant/observer can cope with discontinuities. 11

The obvious precedent for such discontinuity is that of film, which, after preliminary attempts to simulate live theatre, has evolved into a genre incorporating spatial and temporal montage. I would argue that virtual environments are in a similar stage of development to early film and that it that a 'language' for interacting within virtual environments will likewise evolve. One can anticipate that visual and aural senses will be adequately catered for, and it is not beyond the realms of imagination that approximations of such phenomena as air movement, temperature, texture, and incline will be simulated. The approximations will be discontinuous between spaces and through time yet, just as we have learnt to accept such discontinuity in film, so we will also willingly engage with immersive environments. Already what is evident within present examples, such as CAVE, is the potential to supersede the 'perspective snapshot' as the means by which architecture is developed and appraised.

Computer Aided Construction
Techniques of emergence and developments in computer simulation described above have the potential to allow an architect to evade the 'projective transactions' between perception and orthographic and perspective drawing. What remains of Evans' tetrahedral model are the transactions between representation and the realization of the actual architecture.

Digital models used in such applications as CAVE exist as three-dimensional mathematical descriptions, precisely the format required to bring computer numeric controlled (CNC) machines to life. Frank Gehry's recent Bilbao Museum is perhaps the highest profile building to be realized via such machines. Bilbao was initially conceived via a cardboard model and then, utilizing 3D digitizing techniques, an accurate computer model was generated. The outline model was supplied to engineers who devised a series of vertically stacked trusses that closely follow the curving wall profiles. Prior to construction a scale model was produced with computer controlled milling machines to allow the architect to compare the developed project with the original cardboard model. The project was then realized by transmitting the computer files to the fabricators who utilized C.N.C. machines to cut the structural steel and titanium cladding panels.

During this conception and development there was no engagement with historical methods of representation as defined by Evans. The project was conceived in a physical medium, developed utilizing digital models, appraised via a computer generated physical model and realized by transmitting digital instructions to CNC machines.

The importance of Bilbao is that it marks a fundamental shift in the relationship between representation and construction. Unlike forms of art or science where medium and object are concurrent, architecture normally operates at least twice removed from its object - the architectural project is developed in a representational medium (traditionally drawing) and then realized via the filter of scaled plans and sections. The working methods utilized for the Bilboa project enabled Gehry to in effect work directly with the final architectural object. Gehry describes this experience in terms of craft.

In the past, there were many layers between the rough sketch and the final building, and the feeling of the design could get lost before it reached the craftsman. It feels like I've been speaking a foreign language, and now, all of a sudden, the craftsman understands me. 12

The impact on Evans' diagram of such a working paradigm is substantial. Orthographic projection as the means to convey information to the construction industry is made redundant. Dimensioned plans, elevations and sections are substituted by digital information that can be used to generate scale models for evaluation purposes and to realize the project via CNC machines.

Impact of digital machines on Projection and its Analogues
The impact of emergence, immersive editing and computer aided construction on each of the transitive paths of Evans' diagram is summarized below (Fig. 1).

Transitions between designer and the designed object (7)

As discussed in the example of Latham and Todd the transition from designer to emergent form is largely outside Evans' web of projective transactions. It may be possible to visualize some of the expected outcome but emergent form is by definition unforeseeable. While highly unlikely, this 'unseen form' could be implemented via C.N.C. machines to directly produce architecture without editing via projection. In a reverse process it would be possible to take existing building and use these as the 'gene pool' for further mutations.

Transitions between designer, orthographic and perspective drawing (2, 4, 6)

It has been shown that it is possible for drawn orthographic and perspective projection to be replaced by the immersive editing of computer models. Ideas can potentially be developed by designing while 'occupying' the model. The experience would be totally immersive and interactive. Such visual systems exist, aural systems are well advanced and it is anticipated that most sensorial experience will be likewise synthetically stimulated. It is not expected to match the sophistication of human senses. It would be satisfactory to induce an augmented version of the experience induced by cinema. The digital model would function as the new work space for the editing of architectural form and space and allow the testing of program requirements, all from the point of view of inhabitation.

Transitions between orthographic and perspective drawing and designed object (3)

The existing practice of translating architecture to scaled two-dimensional drawing to enable physical construction has been removed. The designed digital model would be 're-constructed' by C.N.C. machines that translate the digital code to reproduce the model in physical form. In addition the need to produce fixed perspective views of proposed building is removed by use of the real time digital model. In a reverse direction existing or demolished buildings can be 'experienced' via the digital model.



Figure 4: Collapsing the Tetrahedron, Moloney 1999

Collapsing the Tetrahedron: Architecture with(in) Digital Machines
In summary the alternate procedures outlined above - emergence, immersive editing and computer aided construction - allow a re-evaluation of Evans' framework. The nodes of Evans diagram dissolve and the distinction between designer, digital model and realized project is blurred. Perhaps to the extent that the designer in effect works directly with the final architectural object as opposed to 'action at a distance' via drawing. Hence it can be proposed that the use of digital 'machines' allow a sense of working on the architecture as against working with representations of the architecture. The impact of the above arguments is that the tetrahedral model proposed by Evans is at the point of collapse. As suggested in Figure 4 the nodes dissolve and the distinction between designer, emergent form, immersive model and architecture are blurred.

In an extreme version it has been demonstrated that architecture can be conceived, developed and manufactured without recourse to any systems of projection, drawn or otherwise. This is not to suggest the architecture had not been designed. In this direct path between emergent and architectural form the activity of the designer is directed towards the design of parameters within which form evolves. A more likely version would involve the subjective evaluation and editing of these models generated by emergent systems. Design in this case would involve both the parameters and the intuitive manipulation of the model with(in) the digital machine. In both cases CNC machines can be utilized to construct the designs without the need for translation of the digital model to projective drawings.

As suggested by the examples various paths within this framework are being progressed in isolation in a variety of disciplines. Within architecture Bernard Cache is one who comes close to implementing the full range of possibilities.13 Cache sets form in motion as trigonometric functions, these are evaluated by clients on the internet via video images, and realized as designed objects by transferring code directly to C.N.C. machines. The output of Cache and his collaborators is modest (furniture and various machined panels) but the implications of the process are wide ranging. Not the least for historians who will document the architecture of the twenty-first century.

Notes
1 Evans, R. (1997), Translations from Drawing to Building and other essays, London, Architectural Association.

2 Evans, R. (1995), The Projective Cast: Architecture and its Three Geometries, pp.147-158, London and Cambridge, M.I.T. Press.

3 Evans, R. (1995), Ibid pp.179-202.

4 Evans, R. (1995), Ibid pp.305-314.

5 Evans, R. (1995), Ibid p.363

6 Evans, R. (1995), Ibidp.369.

7 Todd, S. and Latham, W. (1992), Evolutionary Art and Computers, p.6, London, Academic Press Ltd.

8 Todd, S. and Latham, W. (1992), Ibid, p. 98.

9 Developed by the Electronics visualisation laboratory at the University of Illinnois in 1992 CAVE are now in use for scientific research and visualisation within a number of institutions world wide. See the CAVE research network for ongoing applications. http://www.evl.uic.edu/cavern/vrserver.html.

10 As an example of such criticism see Cheng, N.Y. (1995), 'Linking the Virtual to Reality', pp.303-311 in CADD Futures 1995, Singapore: National University of Singapore.

11 Bridges, A. (1995), 'Design Precedents for Virtual Worlds', p.300 in CADD Futures 1995, Singapore: National University of Singapore.

12 Gehry, F. (1992) 'Gehry Forges New Computer Links', p.105 in Architecture V.81, Aug. 1992.

13 See Cache, B. (1995), Earth Moves: The Furnishing of Territories, London and Cambridge, M.I.T. Press for theoretical underpinning of his architecture.