Elegant mathematics bending the future of design

Summary

Have you ever rolled a piece of paper into a cylinder, or tried to wrap aluminum foil around an object without making it crumple? Imagine being able to simply turn a piece of flat material into beautiful, strong furniture, lighting or even the buildings and bridges of the future.In the world of architecture and product design this idea of building complex 3D shapes using flat materials has always been a fascinating challenge. Flat sheets made from materials such as paper, metal, or plastic are easy to cut and manipulate, but until now, turning them into specific curved shapes has required clever engineering and design, expensive shaping tools and often a lot of trial and error.C-Tubes Enter C-Tubes, a new way to build curved, tubular structures using flat strips that bend without stretching or wrinkling, developed by researchers from the Geometric Computing Laboratory (GCM) part of EPFL’s School of Computer and Communication Sciences (IC). Their paper, C-Tubes: Design and Optimization of Tubular Structures Composed of Developable Strips, was presented this week at the ACM SIGGRAPH 2025 Conference, receiving the Best Paper honorable mention.“In architecture, engineering and design, surfaces you can make from flat sheets of material are called developable. A sheet of paper, for example, can be rolled into a cylinder or a cone without damaging it,” explained Klara Mundilova, a post-doctoral researcher at GCM. “Designing with developable surfaces is tricky—most methods require careful tuning to avoid creases or distortions. We take a different route and assemble parts that are developable by construction,” she continued.The researchers came up with a system where they cut flat strips from a sheet, then bend and connect them to form closed tubes that curve, twist, and loop in space. These C-Tubes are surprisingly stiff and strong, even though they’re made from materials that are flexible before assembly.VIDEOBehind this simplicity lies elegant mathematics, and the underl...