Repetitive Surface Structures Designing gridshells with asymptotic line networks

INSIDE\OUT Pavillon in the courtyard at the TU München

Repetitive Surface Structures is a research studio held annually at the Chair of Structural Design. We are searching for methods to simplify the construction of double curved surfaces. Through physical and computational experiments we demonstrate new possibilities for an intelligent symbiosis of form, structure and fabrication. Our current research investigates three specific types of curve networks: Asymptotic Lines, Geodesic Lines and Principle Curvature Lines. Each of these networks has the property of omitting a certain curvature type. This has great benefits for fabrication and assembly.

  • Asymptotic Lines have no normal curvature. They can be constructed from straight strips orthogonal to the surface.
  • Geodesic Lines have no geodesic curvature. They can be constructed from straight strips tangential to the surface.
  • Principal Curvature Lines have no geodesic torsion. All joints are orthogonal. Both orthogonal and tangential strips are developable.
Shown above are specific line networks, which are based on a constant value k=0 of either their normal curvature, geodesic curvature or geodesic torsion. This has an influence on the constructibility, as indicated by the bending or twisting of the respective profiles.


Asymptotic Gridshell is a design proposal of a pavilion for the Structural Membranes Conference 2017 in Munich. The design takes a clipping of a repetitive, cubic Schwarz D minimal surface, to generate an expressive sculptural space. The support structure follows a curve network of asymptotic lines. All elements can be constructed out of straight strips with orthogonal nodes. The ongoing research investigates material use, structural performance and assembly methods for this new type of gridshell.

Prototype model at scale 1:5. A network of asymptotic lines on a clipping of a minimal Schwarz D surface. The support structure was constructed from straight strips of beech veneer. All joints are identical and orthogonal. Model: Denis Hitrec; Foto: Denis Hitrec