Building better, building beautiful
Novel method allows more architects to design attractive gridshell structures
image:
An example of a gridshell with a topologically irregular boundary shape computed with the proposed system. ©2025 Masaaki Miki and Toby Mitchell CC-BY-ND
view moreCredit: ©2025 Masaaki Miki and Toby Mitchell CC-BY-ND
A researcher from the University of Tokyo and a U.S.-based structural engineer developed a new computational form-finding method that could change how architects and engineers design lightweight and free-form structures covering large spaces. The technique specifically helps create gridshells, thin, curved surfaces whose members form a networked grid. The method makes use of NURBS surfaces, a widely used surface representation format in computer-aided design (CAD). It also drastically reduces computation cost — a task that previously took 90 hours on a high-end GPU completes in about 90 minutes on a standard CPU.
Architects pay particular attention to surfaces capable of supporting their own weight. Some aesthetically pleasing structures are called shells, traditionally realized as reinforced concrete shells. However, contemporary architects aim to reduce the use of concrete due to costs and wastage, and also as they wish to use more attractive materials, including glass. This has encouraged architects to explore what are known as gridshell designs, architectural structures made from intersecting curved metal, glass or timber sections that span wide spaces without internal supports.
Gridshells are good for covering large public spaces without the use of interior columns, such as train station entrance halls, renovated courtyards of historic buildings, and public plazas. Familiar examples include the British Museum’s Great Court, the Dutch Maritime Museum’s glass roof and Moynihan Train Hall in New York. These projects demonstrate the potential of gridshells, but until now, there have been no standardized computational methods capable of efficiently handling the full range of possible shapes that architectural designers may wish to create.
Masaaki Miki from the University of Tokyo and Toby Mitchell, who works at U.S.-based engineering firm Thornton Tomasetti, teamed up to develop a technique that gives architects and engineers more creative freedom. Their new algorithm finds the optimal shapes of gridshells, capable of handling complex shapes without sacrificing robustness.
Though precedents of gridshell projects exist in the world, various constraints from geometry, mechanics, fabrication and construction required to create them have made gridshells impractical for most clients. Miki and Mitchell previously developed a novel NURBS-based method that solves these constraints within a single universal computational framework. However, two key barriers remained: Their previous algorithm could not handle highly irregular shapes, and the computational cost was unrealistically high. Their new method overcomes these barriers, leading to a more accessible and efficient design process, opening up advanced gridshell form-finding to a broader range of designers and architects.
“The project began in 2020 with an interest in shell structures, often made of concrete. Traditional designs aim for shapes that carry their own weight entirely through the force of compression, but this limits how expressive or sculptural they can be,” said Miki. “We set out to find new ways to design shells that consider forces of compression as well as tension, allowing greater design freedom. We adapted our approach to more modern metal-and-glass gridshells, developing methods to balance mechanical reliability, aesthetics and ease of construction. Recent advances in computational speed have made it possible to solve such complex conditions using rigorous methods.”
The major advantage of their method is that it directly operates on NURBS surfaces. Unlike conventional mesh-based modeling that uses thousands of triangular facets, NURBS offer smooth, continuous and mathematically precise surface representations. More importantly, NURBS surfaces are also standard in architectural design. The team integrated their method with an application called Rhinoceros, a popular NURBS-based CAD package, as a plug-in. This means the approach can more easily become part of an architectural designer’s regular workflow.
The core idea of their approach is to represent the distribution of stress using a NURBS surface and some novel algorithms which speed up computation by a dramatic 98%. This increase eliminates the need for high-end GPUs, providing a more accessible method for generating geometrically and mechanically sound gridshells. It also ensures output forms are rigid under gravity and ultimately offers a metal-and-glass construction system which is easy to construct.
“Because we are addressing a real-world problem, we have been rigorously validating our solutions by several test methods we also developed,” said Miki. “When the tests revealed failures in the method, it was stressful. However, we are now totally happy because all solutions pass the tests.”
While the current work focuses on metal-and-glass gridshells, the researchers also aim to extend the method to composite timber gridshells in the future.
Thanks to computer numerical control (CNC) fabrication technologies, the method may also be applied to design-laminated timber gridshells. ©2025 Masaaki Miki and Toby Mitchell CC-BY-ND
Credit
©2025 Masaaki Miki and Toby Mitchell CC-BY-ND
Proceedings: Masaaki Miki and Toby Mitchell, “NURBS-Based Grid Shell Form Finding on Domains with Topologically Arbitrary Boundaries”, Transactions on Graphics Siggraph special issue, DOI:10.1145/3763284, https://www.mmiki.jp/home/project-kannegon
Funding: This research was partially supported by the Nomura Foundation, the JSPS Grants-in-Aid for Scientific Research (KAKENHI; grant number 23K17784), and JST ASPIRE (grant number JPMJAP2401).
Useful links:
Graduate School of Arts and Sciences - https://www.c.u-tokyo.ac.jp/eng_site/
Masaaki Miki - https://www.mmiki.jp/
Thornton Tomasetti - https://www.thorntontomasetti.com/
Research contact:
Assistant Professor Masaaki Miki
Graduate School of Arts and Sciences, The University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo, 153-8902 Japan
masaakim@g.ecc.u-tokyo.ac.jp
Press contact:
Mr. Rohan Mehra
Strategic Communications Group, The University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan
press-releases.adm@gs.mail.u-tokyo.ac.jp
About The University of Tokyo:
The University of Tokyo is Japan's leading university and one of the world's top research universities. The vast research output of some 6,000 researchers is published in the world's top journals across the arts and sciences. Our vibrant student body of around 15,000 undergraduate and 15,000 graduate students includes over 5,000 international students. Find out more at www.u-tokyo.ac.jp/en/ or follow us on X (formerly Twitter) at @UTokyo_News_en.
Method of Research
Computational simulation/modeling
Subject of Research
Not applicable
Article Title
NURBS-Based Grid Shell Form Finding on Domains with Topologically Arbitrary Boundaries
Article Publication Date
3-Dec-2025
