A new NURBS-based algorithm is revolutionizing gridshell design by enabling faster, smoother, and more flexible shape-finding.

What once required 90 hours of GPU time now takes just 90 minutes on a standard CPU, unlocking bold architectural possibilities.

A Faster Way to Shape Lightweight Free-Form Structures

A researcher at the University of Tokyo and a structural engineer based in the United States have created a new computational form-finding method that may significantly influence how large, lightweight architectural structures are designed. The approach is tailored for gridshells, which are thin, curved surfaces formed from a network of intersecting structural members. Their technique relies on NURBS surfaces, a familiar digital surface format in computer-aided design (CAD), and greatly cuts down on the amount of computing required. A process that once needed 90 hours on a high-end GPU now finishes in roughly 90 minutes on a standard CPU.

Architects place great importance on surfaces that can hold their own weight. Many visually striking structures fall into the category of shells, which have traditionally been built from reinforced concrete. Today, however, designers are trying to limit concrete use because of cost, waste, and growing interest in more transparent or visually appealing materials such as glass. This shift has encouraged wider exploration of gridshells, which use intersecting curves made of metal, glass or timber to span large areas without internal supports.

Why Gridshells Are Attractive for Large Public Spaces

Gridshell structures work well for covering broad interiors without columns. They appear in locations such as train station entrances, updated courtyards in historic buildings, and open public plazas. Well-known examples include the British Museum’s Great Court, the glass roof of the Dutch Maritime Museum, and the Moynihan Train Hall in New York. While these projects show how effective gridshells can be, designers have lacked a standardized computational method capable of handling the full variety of shapes they would like to produce.

Masaaki Miki of the University of Tokyo and Toby Mitchell of the U.S. engineering firm Thornton Tomasetti collaborated on a technique that offers far more freedom in shaping these structures. Their algorithm identifies the optimal geometry for gridshells, even when the overall form is highly complex, while still maintaining structural reliability.

Removing Barriers That Once Limited Gridshell Design

Although gridshells have been built before, the geometric, structural, fabrication, and construction constraints involved have made them unrealistic for many clients. Miki and Mitchell had previously introduced a NURBS-based approach that addressed many of these difficulties within one computational framework. Two obstacles, however, remained: their earlier method struggled with very irregular shapes, and the computing time required was too long for practical use. The new version resolves both issues, creating a more efficient and accessible workflow and allowing many more designers to engage with advanced gridshell form-finding.

“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.”

Working Directly With NURBS Surfaces for Better Workflow Integration

A key strength of the updated method is that it works directly on NURBS surfaces. Traditional mesh-based modeling relies on thousands of triangular elements, but NURBS provide smooth, continuous and highly precise surface representations. They are also widely used in architectural design. The researchers incorporated their technique into Rhinoceros, a commonly used NURBS-focused CAD platform, as a plug-in. This integration allows architects to adopt the method more easily in everyday practice.

The central concept behind the method is to capture stress distribution using a NURBS surface together with new algorithms that improve computation speed by 98%. This efficiency removes the need for high-end GPUs and offers a more accessible path for producing gridshells that meet both geometric and structural requirements. The resulting shapes remain stable under gravity and support metal-and-glass construction that is practical to build.

“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.”

Extending the Method Beyond Metal-and-Glass Designs

Although the current work centers on metal-and-glass gridshells, the team intends to expand the method to composite timber gridshells in the future.