CNets | C-tubes
- CNets: An Interactive Design Framework for Cone-Nets
- Advances in Architectural Geometry 2025
Planar quadrilateral (PQ) meshes play an important role in Architectural Geometry, with ongoing research focused on developing effective tools for their design. Cone-nets are a special class of regular PQ meshes in which one family of PQ strips forms discrete (projective) cones. This paper builds on recent advances in the study of cone-nets and presents a constructive implementation in an interactive design tool that enables intuitive real-time exploration of the design space of cone-nets within the Grasshopper/Rhino environment. We provide novel theoretical insights into cone-nets, introduce a user-friendly interface, and incorporate a correction mechanism to repair degenerate configurations. Our aim is to make cone-nets more accessible to the broader community of practitioners and to promote their application in advanced architectural design scenarios.
Examples demonstrating incremental use of the design flexibility of the CNets Construct plugin.
Architectural facade with PQ faces and torsion-free support structure designed using our CNets plugin.
Manual design of a catamaran hull using our CNets plugin.
CNet Pedestrian bridge. Our construction ensures the deck, the girders, and the glass panels are developable.
- C-Tubes: Design and Optimization of Tubular Structures Composed of Developable Strips
- ACM Transactions on Graphics, SIGGRAPH 2025
We introduce C-tubes, 3D tubular structures composed of developable surface strips. C-tubes can be understood as a generalization of Monge surfaces—a special class of sweep surfaces—towards the recently introduced cone-nets. This observation allows formulating a constructive algorithm to create tubular structures that ensures developability of the constituent surfaces, while significantly broadening the design space. Our novel form-finding tool enables design exploration by solving for the input variables of the constructive algorithm so that the C-tube best conforms to user-specified objectives. We discuss several case studies that illustrate the versatility of our approach for the design and fabrication of complex structures, with applications in architecture, furniture, and lighting design.
A tube generated by rotation-minimizing frames (left) vs a C-tube (right).
Resources
CNets
Paper
Advances in Architectural Geometry 2025
Code
Rhino Grasshopper plugin for interactive CNet design.
C-tubes
News
Elegant Mathematics Bending the Future of Design
Acknowledgements
We gratefully acknowledge Erik Demaine and Tomohiro Tachi, whose idea of using scale mappings to encode the locations of cone apices forms the basis of our construction. We thank Liliane-Joy Dandy, Filip Goč, Oliver Gross, Uday Kusupati, Seiichi Suzuki, and Kurt Wettstein for their assistance with fabrication and valuable discussions. This research was funded by the Swiss National Science Foundation (SNSF), grant numbers 200021-231293 and 200021-188582. Klara Mundilova is supported by the Swiss Government Excellence Scholarship.