Shaped by Number
Kenneth Wong
Issue: Volume 33 Issue 9: (October 2010)

Shaped by Number

About three kilometers southeast of La Sagrada Familia (Barcelona, Spain), behind a red terra-cotta door on Carrer de Pujades, a small army—a force of 100, led by 25 captains—labored deep into the night inside a spacious studio that belonged to the Institute for Advanced Architecture of Catalonia (IaaC). While Spanish youths reveled in tapas and sangria along the long, tree-lined pedestrian walkway of La Rambla, the indoor crowd wrestled with cardboard cutouts, wooden blocks, stretched fabrics, and foam trimmings. Some stared at glowing laptop screens, hoping to unlock geo­metric mysteries. Others wrote strings of code to conjure up strange shapes. Many worked around the clock, for­going sleep, fueled by café solos. They represented a sampling of the brightest minds from world-renowned design firms (Foster+Partners, KPF Kohn Pedersen Fox, Grimshaw, Arup, Buro Happold) and academia (Architectural Association, MIT, Delft Technical University, University of Bath). They were the wizards of computational design, the SmartGeometry Group (, in action.

The parametric fabrication model was developed from the original surface geometry for Centre Pompidou, Metz. This model was built using the Autodesk DesignComputation prototype software to show that it is possible to explore a range of design and modeling strategies.

Like a traveling circus, the annual SmartGeometry workshop and symposium moves from city to city, giving participants a chance to flex their creative muscles in a new location. Last year, it was San Francisco; this year, it was on famed Catalan architect Antoni Gaudi’s home turf: Barcelona.

In 2001, the year explicitly referenced in the title of Arthur C. Clark’s futuristic yarn, SmartGeometry Group was formed. On its Internet home page, the group proclaims, “To the new generations of architects, mathematics and algorithms are becoming as natural as pen and pencil. The activities of the SmartGeometry Group promote the emergence of a new generation of digital designers and craftsmen, who are able to exploit the combination of digital and physical media. The group’s interests range from parametric design and scripting to digital manufacturing.”

Their mission gave rise to a series of design methods, almost as fanciful as science fiction. This year’s workshop exercises explored, for example, tensile membrane systems, inflated fabric volumes, and identical blocks that could be snapped into place. Translated into architectural and engineering concepts, they might mean rooftops and curtain walls shaped like wind-filled kites and sails, or modular pegs and posts that can be joined together to form support structures without welding.

The standard approach in computer-aided design (CAD) is to use a specialized 3D modeling package—for instance, Graphisoft’s

ArchiCAD or Autodesk’s Revit for buildings; Dassault Systemes’ Catia, Parametric Technology’s (PTC) Pro/Engineer, or Siemens’ NX for automotive and aerospace—to produce a digital replica of an idea. You decide the width of every window and door; you specify the radius of every arc.

However, with computational design, you do not dictate every minute detail of your design; instead, you define the design criteria (for example, an acceptable range for width, a desirable number of curves, with angular deviations by a certain degree), then let the software generate various permutations from which you can choose. The recipe—a mix of scripting and modeling—often produces something unforeseen by the designers themselves.

Pictured here is a series of room-enclosure strategies explored by the SmartGeometry workshop group while studying acoustic surfaces.  Image courtesy of SmartGeometry Group and Bentley Systems.

Singing Rooms; Quiet Rooms

Brady Peters knows how to make a room sing—or muffle it entirely. In his curriculum vitae, he explains his research focus: “[My] current research investigates new interfaces between acoustic science and architectural design.… By investigating how architec­tural surfaces, such as walls, floors, and ceilings, can be designed and detailed to be acoustically regulating, the project aims to develop integrated design solutions for sound in architecture.”

Peters is a PhD fellow at the Center for Information Technology and Architecture (CITA) and an architectural researcher with JJW Arkitekter and with Grontmij/CarlBro Engineers. He has flown in from Copen­hagen, Denmark, to lead a SmartGeometry workshop cluster (a small team of 10 to 15) devoted to manufacturing parametric acoustic surfaces. In this intense three-day experiment, the team under his tutelage set out to understand how the composition of a room affects resonant absorption and sound scattering. Aside from the common construction materials at their disposal (cardboards, foam, sheet metal, wood, and so forth), they used Bentley’s Generative Components (GC) software and Odeon’s acoustic analysis software. In his own work, Peters also uses custom computer programs written in Visual Basic or C#, along with Bentley’s MicroStation.

“Sound waves occur at different frequencies—this is what we hear as low or high sounds,” Peters says. “Low sounds have much longer wavelengths than high sounds. The material of a surface determines the amount of sound that is absorbed, [while] the geometry of the surface determines the direction in which it is reflected, and the size of the surface determines the size of wavelengths that it reflects.”

Explaining the guiding principles for building acoustic surfaces, Peters notes,

“Wallace Sabine, a Harvard scientist, determined that the reverberation time, the time it takes for sound to decay to inaudibility, is one of the most important in determining the acoustic performance of a space. His equation for determining reverberation time from the material properties is one that must be considered. For determining reflections, I use a raytracing algorithm. Using geometry generated in CAD software and either acoustic analysis software or custom computer scripts, I can determine the amount of sound getting from a source to a receiver.”

Using GC, acoustic surfaces workshop participants came up with various room shapes, distinguished by different degrees of enclosure. Based on acoustic analysis results showing sound-pressure levels and early decay time for each room composition, the team chose a model enclosed in an S-shape curve. Peters knew from his research that complex geometries with many edges and a variety of surface depths constructed from hard materials tend to diffuse sound. By contrast,

alternating wedge-shaped forms constructed from foam will absorb sound; and large, flat surfaces of concrete, metal, plywood, and other hard materials will reflect sound.

“The absorbing qualities of the orange acoustic foam created a dull space where all sound reflections were absorbed by surrounding walls,” Peters explains. “A performance gradient from a totally absorbing to a totally reflecting surface was created through variation in panel perforations. An amplified space was created by using raytracing to predict sound reflections focused at a single point. A scattered sound space was created by having complex geometries that would scatter sound waves and not allow distinct echoes to be heard.”

Thus, by careful texturing the enclosures in geometric patterns, the team further controlled sound behavior in each chamber. For an area of the enclosure with recursive holes (an aesthetic treatment), the team once more turned to GC to automatically generate the hole patterns, then use a computer numerical control (CNC) laser cutter to cut the patterns.

Playground at a Glance

In computational design discussions, the names of two software packages—Bentley’s GC and Robert McNeel & Associates’ Grasshopper—tend to crop up often. GC is tightly integrated with Bentley’s flagship product, MicroStation, but a stand-alone version is also available, currently downloadable free of charge. Grasshopper is a plug-in to McNeel’s popular NURBS modeler Rhino and available as a free download for Rhino users.

While GC lets users refine designs through dynamically modeling and directly manipulating geometry, it also uses a C-style programming language to record and store feature sets “under the hood,” such as the curvature of a spiral staircase’s railing or the individual plates that comprise the steps. Iterations are driven by transaction definitions, which are also scripted. This method allows users to create, for instance, a high-rise tower whose shape is defined by a stack of hexagons. By alternating the sizes and angles of the skeletal hexagons and the distance between them, architects and designers may continue to create variations of the same tower derived from the same set of rules.

As a result, they are able to bypass the process of modeling each altered component of the design by hand. Instead, they can refine or edit designs by directly manipulating those features, or by working under the hood and editing the transactions and scripts directly. A case in point is work by the SmartGeometry cluster exploring acoustic surfaces: The group didn’t have to sketch each wall hole; the patterns were automatically generated based on a set of rules.

GC comes with an integrated development environment and a debugger—familiar tools for programmers but perhaps not so much for architects used to working with solid shapes, splines, lines, and arcs.

Rhino plug-in Grasshopper allows architects to create geometry in a similar fashion, with an interface that is more graphical. All the rules governing the geometry generation (or regeneration) process—base profile, logic, vector lines, equations, Boolean operations, and so forth—are embedded in drag-and-drop icons, allowing designers to work in a flowchart-like environment. The designers are still developing scripts, but the operation happens in the background, behind the visible canvas.

Another contender for generative design is currently in development at Autodesk. The initiative is led by Robert Aish, the silver-bearded Obi-Wan Kenobi of computational design. In his former role as Bentley’s director of research, he once shepherded the early development of generative computation. His departure from Bentley in 2007 stirred fans of this particular design process—so much so that Lars Hesselgren, a veteran of the SmartGeometry Group, was prompted to offer assurance in a blog post at

Above shows the shape of the acoustic-enhanced room designed by the SmartGeometry workshop group, as rendered in Bentley’s Generative Components software.

“We have to acknowledge the enormous role Robert played in creating GC. It was very much his baby. Autodesk’s move underlines the acceptance into the marketplace of tools designed for the new design age, where computers are used as active design participants. It is a fundamentally different concept from BIM (building information modeling). From all the reactions I have had so far, it is clear that GC will carry on without dad. Being brought up by foster parents, he will be different. We can look at it as an experiment in the ‘nature versus nurture’ debate. We, the GC users, hope to nurture him through adolescence to a fully mature and rounded young man. And we wish dad the best of luck in his new life.”

Aish won’t get into details about the contrast between his work at Bentley and his work at Autodesk, except to say, “If an architect builds a brilliant sports stadium, and a few years later another client comes along and asks, ‘Can you build me one just like that?,’ then the architect, if he’s got any gumption and creativity, would say, ‘Nope, I won’t do the same thing again; I’d like to do something different.’ ”

The debut of the new technology will most likely be inside AutoCAD, Autodesk’s rival product to Bentley’s MicroStation. Autodesk doesn’t have a specific time frame for delivering the software, but Autodesk customers have had glimpses of the technology at Autodesk University (AU) 2009, first in a computa­tional design symposium and later during CEO Carl Bass’s main stage presentation.

“Our whole intention is to provide a gentle learning curve, where you start off with sketching,” says Aish. “The software is writing the script for you under the hood. You don’t even need to know we’re doing that for you. But if you say, ‘Now that I’ve drawn the curves and lines, I’d like to do something to every other curve,’ then we can open the panel to show you a more complicated set of controls. But that’s optional.”

This tessellated profile was created by Hyoung-gul Kook using the Rhino plug-in Grasshopper. This is the code used to create the profile.

Powerful Playthings

Daniel Piker, a recent graduate of The Architectural Association in London, maintains the Space Symmetry Structure blog (, summarized as “journeys in the Apeiron,” a reference to a sixth-century cosmological theory. Along his so-called journey, he is delving into shape possibilities springing from relaxation of the tensile strength. To visualize Piker’s geometric fascination, one might imagine a melting wire cage or a drooping fishing net. His other fascination (which he admits has been gathering dust for a while) is deployable, transformable structures, resembling folded—and re-foldable—patterns found in origami. If you accuse him of frivolous pursuits, the mild-mannered, soft-spoken Piker will tell you, “Toys can be tools—both playful and powerful.”

In January, Piker announced the birth of Kangaroo, his own plug-in to the Rhino plug-in Grasshopper. In essence, Kangaroo is a physics engine that lets users apply several types of forces, which he wrote from scratch. Piker’s creation is now available for download at

“With Kangaroo, the physics run interactively, so the model can be manipulated ‘live’ while the simulation is running,” he explains. “This lets the user engage with it in a direct and intuitive way. It is designed to be easy to learn and use, requiring zero programming or engineering knowledge, while still allowing a high degree of control.”

It is mesmerizing to watch the geometric deformations driven by Kangaroo, but don’t dismiss it as a pointless programming exercise. “Kangaroo is primarily intended as a tool for designing buildable structures, not just creating animations,” Piker points out. “Catenary grid shells and tensile structures, such as fabric canopies, are the most familiar application for [deploying Kangaroo-generated geometry in real life], but I think that is just the tip of the iceberg [potentially leading to] generating forms that deal with forces in elegant and efficient ways, copying and adapting natural processes such as plant growth or crystal formation.”

Fishpond for Architects

Another Grasshopper user, Hyoung-gul Kook, recently graduated from Columbia University’s Graduate School of Architecture, Planning, and Preservation, and is now employed at Weiss/Manfredi Architecture. Like Piker, he, too, chronicles his geometric experiments. In his Live Components blog, he wrote: “Through my recent researches and practices, I’ve been developing various geometries in easier ways. These definitions are based on simple mathematical knowledge and reasonable logic without any scripting.” Live Components is essentially an archive of geometric definitions, ready to be used in Rhino and Grasshopper.

“It is not a fish, but the knowledge of how to fish,” Kook says about his methodology.

One of his definitions produces tessellated folding structures, something already common in modern architecture. “Folding provides not only aesthetic visions, but also structural strength and spatial sensation in architecture,” Kook explains. “Depending on the scale, it could be anything from small pavilions or shading devices to large stadiums or convention centers.” As examples, he points to the Yokohama International Port Terminal (by Foreign Office Architects) and the Air Force Academy Chapel (by Skidmore, Owings & Merill LLP).

Digital Fabrication

It’s not a coincidence that SmartGeometry enjoys the sponsorship and attendance of prominent digital fabrication technology developers and suppliers, including 3D printer maker

Z Corp., 3D printer reseller ZSI Nuevas Tecnologias, and robotic building maker D-Shape. The geometry produced using computational design involves modulated surfaces, parametric variations, and shape deviations so sophisticated that, to reproduce it in the real world in an efficient manner, users would have to rely on computer-controlled cutting devices.

“Recent digital technologies and fabrication tools have made it possible to tessellate any

geometry to be built by using non-standardized modulations,” Kook points out. In Smart­Geometry workshops, digital fabrication was the only way for many participants to transform their digital visions into physical form, to be cut, assembled, and put on display so the audience could admire them on the final day of the event. The acoustic surfaces cluster used a computer-controlled machine to mill sound-scattering surfaces out of Alucobond.

This screen shot shows Bentley Systems’ Generative Components, one of the primary computational design software programs used by SmartGeometry workshop participants.

Purposeful Algorithms

At present, many architectural designers use script-driven design tools to experiment while mathematically deforming solids and surfaces into never-before-seen shapes, but as computational design matures, we can expect practitioners to use it for much more than aesthetics. The set of rules governing the iterative process could easily be linked to a building’s energy performance or structural integrity.

“The use of generative design methods is clearly helping architects and engineers deliver inspiring, more sustainable, higher performing buildings—in other words, buildings that are far superior aesthetically, structurally, and functionally,” says Huw Roberts, Bentley’s global marketing director. “The time invested by the many participants at the SmartGeometry 2010 Workshop and Conference in Barcelona exemplifies the interest the architectural and engineering professions have in exploring the potential benefits and applicability of this technology-empowered methodology.”

SmartGeometry workshop leader Brady Peters recalls a project he worked on at Foster and Partners: the Smithsonian Courtyard enclosure in Washington, DC, which featured a new roof structure over the previously open courtyard.

“The desire for this space to be used for concerts and receptions led to a specification in terms of acoustic absorption. The roof structure was the only place to put the absorbing material,” Peters says. “This complex roof structure was designed using parametric design software and included parameters that controlled the amount of absorbing material. In this way, the form of the roof was linked to its acoustic performance.”

For the SmartGeometry Group, and other like-minded designers, the advantages of generative design methods certainly add up—particularly considering that the goal of number-driven geometry is to be purpose-driven.

Kenneth Wong is a freelance writer who focuses on the computer game and CAD industries, exploring innovative usage of technology and its implications. He can be reached at

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