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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.