Computational Design and Optimisation of Quad Meshes Based on Diagonal Meshes

Type: Conference Paper
Year: 2021
Authors: Caigui Jiang, Cheng Wang, Eike Schling, Helmut Pottmann
Published in: Advances in Architectural Geometry 2021. Paris, pp. 38-60
Editors: Olivier Baverel, Helmut Pottmann, Caitlin Mueller, Tomohiro Tachi
Collaboration: KAUST, University of Hong Kong

A significant amount of research in Architectural Geometry has dealt with skins and structures which follow a quadrilateral layout with double curvature. In many cases, such quad networks are computationally accessed by quad meshes which obey various constraints. These may concern planarity of faces, supporting structures which follow specific curvature paths, conditions on node angles, static equilibrium and others.

In this paper we draw the attention to a new way of computing such constrained quad meshes. The new methodology is based on the diagonal meshes of a quad mesh and the checkerboard pattern of parallelograms one obtains by subdividing a quad mesh at its edge midpoints. The new approach is easy to understand and implement. It simplifies the transfer from the familiar theory of smooth surfaces to the discrete setting of quad meshes. This is illustrated with planar quad meshes and asymptotic nets, in particular with those exhibiting a constant node angle.

The application of such networks has advanced fabrication-aware-design in the architectural practice. Looking at asymptotic nets specifically, we list their potentials and challenges for the construction of strained gridshells. The benefits of constant node angles are highlighted along different construction methods in timber and steel. We conclude with current developments, looking at less-restricted and transformable asymptotic structures, and how they are designed.


Quad meshes, mesh optimization, constrained meshes, asymptotic curves, construction-aware design, gridshells

A-nets with constant angle 60° (top), 75° (middle) and 90° (bottom). They represent surfaces with constant principal curvature ratio k1/k2 = C with C = −1/3 (top), C = −0.58879 (middle) and C = −1 (bottom). The latter surface is a minimal surface. Left: One diagonal mesh and the associated checkerboard pattern. Right: The diagonal mesh has been used as a basis for an asymptotic gridshell with constant node angle.

About eikeschling

Dr.-Ing. | Architect BYAK Assistant Professor in Architectural Structures The University of Hong Kong

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: