Observations on the Nature of. Computational Geometry

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1 Observations on the Nature of Computational Geometry Arch 486 Computational Geometry, Spring Qtr The University of Washington Kevin R. Conway Introduction Since beginning graduate studies at the University of Washington, one concept more than any other has been the focus: computational geometry. Barely a day goes by when the term is not offered as part of some discussion. There is Generative Components software, Grasshopper software for Rhino and recently Processing has been presented as a potential computational geometry software tool. Considering that the specific program I have joined at the University of Washington is focused on Design Computing, it shouldn t be a surprise that computational geometry is such a significant part of it. To be sure, there is a considerable amount of information on the internet if one googles computational geometry. What has been a surprise for me, though, is the absolute dearth of architectural projects (built or in process) that are presented as having been designed using computational geometry. There are many images of models and renderings of fantastic looking structures offered by the above mentioned google search but nary a real building. Discussion

2 Of those real buildings offered, some additional research seems to suggest that they had little to do with computational geometry. Rather, they end up with a tag for computational geometry because they used various digital design techniques in their design. To fairly discuss computational geometry I believe that we have to define it more succinctly then it seems to usually be. Computational geometry or Generative design is not about designing a building," explains Lars Hesselgren (Kohn Peterson Fox Associates), "It's about designing the system that designs a building.". In other words, using Grasshopper for example, a designer creates a icon based logic diagram that will then act upon provided data and return structured data (usually in the form of a 3d model) that represents the original data transformed by the logic diagram. Because the process is iterative, the opportunity exists for multiple sets of data to be processed resulting in alternate solutions that still conform to the structure of the Grasshopper logic diagram. Conceivably, an unlimited number of alternatives could be generated as solutions. This is what Generative Components, Grasshopper and (and possibly Processing to some degree) do. This needs to be differentiated from 3d modeling such as that done by SketchUp, 3d Studio, Rhino and many others. These programs manipulate data but based on unique user input (more sculpting than like programming). These programs (in general) don t allow different data sets to be transformed in the same way as an initial model may have been because they do not record the operations performed in a way that allows them to be repeated on subsequent data sets. Also, using digital rendering tools for visualization does not constitute computational geometry either; even if the visualizations provided feedback that resulted in changes to the design. Therefore, 3d modeling and rendering are digital design tools but they are not computational geometry tools. I make this point because many of the projects mentioned above that get tagged as computational geometry, in fact, are only examples of digital design. It should be noted that there is little evidence that the projects suggested as subjects for this paper were actually design using computational geometry. In fact, the Sydney Opera House which was designed in 2/10

3 the mid 1950 s and completed in 1973, probably did not use any computer technology for any part of the design or construction. 1 However, the Sydney Opera House certainly represents the type of form that might respond to computational geometry techniques well. There is a story that the engineers and the architect both labored for about five years to find a method to geometrically describe the overlapping clam shell structures. They considered using Utzon s freehand shapes as templates or parabolic ridges and ribs or parabolic ridges and circular ribs or elliptical ridges and ribs and several other schemes. In the end, Utzon, suggested that each of the clam shell halves could be described as a section of the same sphere. This greatly simplified producing the construction drawings that would describe the geometry. This begs the question: where are the examples of real buildings that have been designed using computational geometry that we could use as subject for this paper? If computational geometry is such an important concept, where is it? At best, computational geometry (at least so far) seems most useful for designing space frame structures or large structures based on repeated elements. And, in fact, these are the very type of images one mostly finds associated with computational geometry. High rise office buildings or curtain wall design may be other areas where computational geometry has some application. This is not to say that computational geometry may not develop in importance and applicability as the technology progresses. With more sophisticated algorithms it may be possible for the technology to provide solutions to buildings that don t depend on large number of repeated elements. Could the technology provide solutions for single family houses? What would the input data be? Would it be the number of occupants or the square footage desired? What variables could be manipulated to drive alternative solutions? An interesting aspect of this line of thought is the seemingly obvious connection to (the now widely discredited) theories of shape grammar first proposed in the fifties and sixties. Is computational geometry just the latest iteration of shape grammar? If so, does it have the same limitations the original theories had or has it evolved to something that may be useful? 1 At most, it may have had engineering calculations performed or checked using an old mainframe, punch cards and Fortran but I doubt it. 3/10

4 Computational geometry techniques do seem to beg the question of whether architects and designers would be willing to give up their creative control to software (which was a concern with the original shape grammar). Is the ability to generate almost unlimited design options an advantage or a benefit? Or is the ability of human insight and inspiration to find a reasonable solution without generating endless alternatives the greater advantage? This is an important question considering how many times a new technology is offered that conceivably could do much of the design work that an architect or designer does. I realize that I have perhaps oversimplified some issues and I don t think I have found anyone who is claiming that computational geometry can replace the designer or architect. In fact, computational geometry software is usually presented as just a tool to solve certain types of problems and as such may prove to have great utility. But the passion that some proponents of the technology show when discussing the technology or the sometimes very broad utility the proponents promise should give one pause. Case Study The one building that I found that more than any other seemed to have used computational geometry legitimately in its design is the National Aquatics Center, in Beijing, China. This building provided the stadium for the swimming and other aquatic competitions at the 2008 Olympics. A nighttime view of the National Aquatics Center 4/10

5 Better known as the Water Cube, the buildings design, engineering, and construction is claimed to have depended heavily on computational geometry techniques. Arup (a multinational engineering, design, project management, and consulting firm), PTW (an architectural firm based in Sydney, Australia), and the China State Construction Engineering Corp. (CSCEC, Beijing and Shenzhen) beat out 10 other project groups to win the contract for this prestigious, world-class project. Arup used MicroStation, MicroStation TriForma, Bentley Structural, and Bentley's Generative Components software to develop the unique design based on a natural pattern of soap bubbles and organic cells. Software like Bentley s Generative Components associative and parametric modeling software can be used by architects and engineers to automate design processes and accelerate design iterations. It gives designers and engineers alternative ways to explore building forms without having to manually build detailed design models for each alternative. Nighttime view of the National Aquatic Center with the Bird s nest stadium beyond. Arup spokesperson, J. Parrish (director of ArupSport) explains that by "using parametrics, I was able to investigate far more alternatives. We built version 34 because it was better. But version 1 would have worked fine. Generative design allowed us to get better results in a fraction of the time." 5/10

6 ArupSport provided engineering and design services for both of Beijing's major Olympic venues. Parrish helped pioneer the rapid prototyping face of generative design and began working with Microsoft's Visual Basic and Excel "a useful interface" and MicroStation in the 1970s to design stadiums quickly. By tweaking any of 3,000 4,000 parameters, Parrish was able to quickly compare, for example, various 50,000-seat positioning schemes and optimize them for views, distance from the field, and other factors. (Stocking, 2009) Parrish claims to be able to do in a few hours what used to take weeks to do. And that combined with other new technologies such as real-time rendering and rapid prototyping amounts to a new way of performing architectural design. He claims to arrive at optimum solutions by using side-by-side comparisons of multiple alternatives that are each slightly different, rather than depending on the "flashlight in the dark" of one designer's genius. The Arup spokesman also discussed a complementary approach that is possible. That architects can instead use computational power to find structural solutions that are self-organizing ; derived through genetic algorithms and not designed by an individual. The Water Cube's soap bubble-like structure used this approach. The roof s soap bubble-like structure is clearly visible inside the Water Cube 6/10

7 According to the book Space Craft: Developments in Architectural Computing (Littlefield, 2008), "Irish physicists Denis Weare and Robert Phelan were able to calculate that the most efficient way to divide a space into cells of equal volume while minimizing the surface area between them was to use a stacked arrangement composed of 75% 14-sided shapes and 25% 12-sided shapes." So far so good, but since the resulting structure would have 22,000 steel members connected at 12,000 nodes, generating an actual model based on the idea exceeded the reach of conventional design. (Stocking, 2009) According to the book, to manipulate this complex geometric system dynamically, Arup wrote custom parametric software that automated the drawing and analysis processes. Based on specified design constraints, the algorithm iteratively checked the distribution of forces through the entire structure based on specific member sizes, allowing the team to test different design configurations and receive feedback within 25 minutes. The result was a spectacular building with a sophisticated structure that is optimized in terms of material weight-to-strength ratio, and it was achieved with relative ease. In addition to the structural advantages, Arup estimated that it saved $10 million on design costs alone compared with traditional design methods. (Stocking, 2009) Water Cube detail 7/10

8 The design of the project juxtaposed water and the square 2 as a theme for both the structural and stylistic elements. Conceptually the square box and the interior spaces are carved out of a foaming cluster of bubbles. In the daytime, the Water Cube shines as a blue transparent spectacle, while in the evening it glows like a cube of frozen water from LED-lit bubbles. The Water Cube measures 176m on each side, rising to a height of 31m. It holds 6,000 permanent seats and had capacity for an additional 11,000 temporary seats for Olympic Games spectators. The Water Cube is claimed to have been designed specifically to work in harmony with the circular main (Bird s Nest) Olympic stadium (Herzog & de Meuron ) with the goal of creating a visual "yin and yang" balance. The Water Cube's structural framework is comprised of two parts an internal and external framework. The external structure forms and supports the actual roof, ceiling and walls and is composed of a flat web of rectangular boxed sections. These sections are clad with the inflatable, transparent material known as ethylene tetrafluoroethylene (ETFE). The internal steel frame is based on the unique geometry of biological cells or soap bubbles. The engineers based the soap bubble structural concept on a solution from two Irish professors described above and known as the Weaire-Phelan structure. The recurring pattern of polyhedrons is packed together to occupy a three dimensional space in the most efficient way possible. More than 22,000 stainless steel frame members arranged in the bubble pattern form the sides of the Water Cube The joints of the frame members are welded to more than 12,000 spherical steel nodes. An additional benefit of this frame design is that it is structurally well suited to the local seismic conditions. We realized that a structure based on this unique geometry would be highly repetitive and buildable whilst appearing very organic and random. Indeed such space filling patterns are regularly observed in biological cells and mineral crystals, they are probably the most common structure in nature. Also the ductile space frame that is generated from this geometry is ideally suited to the seismic conditions found in Beijing. Tristram Carfrae - Arup team leader 2 an important and auspicious symbol in Chinese tradition and mythology 8/10

9 The building s skin was designed to respond to the building s lighting and projection systems to create a stunning visual and sensory experience. This state-of-the-art material provides a cost effective and energy efficient exterior cladding solution. Despite its complex organic look, the structure is actually a simple steel space-frame composed of the inner and outer frames mentioned above but this water bubble based geometry provides the illusion of far greater complexity. The structural components are, in fact, highly repetitive highly repetitive; there are three different nodes and four different members. Exterior skin during constructed Model showing the bubble like structure 9/10

10 Conclusion The question remains for me, was the concept of the bubbles already established and then computational geometry procedures used to design the structural system or did computational geometry somehow lead the design team to this solution. My instinct is that the concept of the cube composed of bubbles was established during the preliminary design phase (probably using marker and flimsy) and that the Bentley tools only used to refine the concept. This does not invalidate computational geometry as a tool but again suggests that computational geometry s place is with analysis and structural design. That it probably doesn t provide any creative solutions no matter how many alternatives are generated but that it can do some of the heavy lifting of design by iterating through many variations of an accepted concept to optimize details. This can be a great tool by allowing a more comprehensive evaluation of things that previously were cut short by time constraints. Whether computational geometry will ever live up to some of the hyperbole attached to it remains another question. View of the Water Cube from the Bird s Nest stadium 10/10

11 The author in front of the Water Cube - March 2010 Bibliography Littlefield, D. (2008). Space Craft, Developments in Architectural Computing. London: RIBA Publishing. Stocking, A. W. (2009, Oct. 15). Generative Design Is Changing the Face of Architecture. Retrieved May 22, 2010, from Cadalyst: 11/10