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Teaching Digital to Physical: Geometry Games

Matt Conway

At the core of the architectural design process is geometry, from initial form-finding to construction. Today, complex geometries take shape in digital modeling software without requiring knowledge of the underlying geometric principles. While it’s easier than ever for designers to bring innovative forms from their imaginations into 3D visualizations, translating these abstractions into life-size construction is a different story – a story that hinges on the 2D to 3D transformation.

Not limited by the two dimensional flat plane, digital modeling enables the genesis of any form. However, flat, linear extrusions remain the cornerstone of economical industrial material production. This means that many digitally modeled forms are essentially unbuildable, especially on a budget. What if taking fantastical forms out of the computer can recalibrate designer’s minds to the realities of manufacturing and construction? As a lecturer at the University of Southern California’s Masters of Architecture program, my Descriptive and Computational Geometry class is designed to do just that: introducing two and three year students to geometric techniques for building complex physical forms.

To transcend the knowledge gap between form and construction, students first develop a geometric lexicon. This begins the negotiation between economic advantages of planar building assemblies and dynamic expression of curved forms. We identify three geometric techniques which essentially allow the construction of a 3D shape from a 2D building template. The simplest is developable surfaces which can be unrolled into flat sheets, such as a cone. The second is planar-quad meshable surfaces which can be panelized using their isoparametric curves, for example a Hyperbolic Parabaloid. Lastly, for doubly-curved surfaces, complex panelization techniques were used for shapes such as an Aperiodic Folded Plate.

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The simplest 2D to 3D geometric conversion: flat sheets that can be rolled into 3D shapes, or developable surfaces

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A more ambitious 2D to 3D geometric conversion takes shape with complex paneling.

For the final project, the newly explored lexicon culminates in a Geometry Game where students merge all three techniques to create oversized physical chess pieces. In the ultimate digital to physical test, the pieces are built by hand from laser-cut flat templates that are designed and developed digitally. Our Los Angeles office hosted the class’s final critique. Over a 12’ x 12’ field, 32 fantastic geometric forms descended for a game of chess. The most successful forms saw exceptional craft and precise alignments where the three systems meet and interact.

Across the course, the biggest challenge was instilling knowledge that students can intuitively translate and apply in the future, be it in other college studio projects or in real-world design like Google Bayview solar design, the 590-foot Baoshan Long Beach Tower, and Jacksonville Museum of Science and History. As designers, pushing beyond boxes can start with the simple plane.

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The Geometry Game underway between the two and three year students.

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Matt Conway
Connect with me to start a conversation ➔ Matt Conway, Computational Design Leader

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