Digital and automatic design of free-form single-layer grid structures

Zhi Li, Jun Ye, Boqing Gao, Qisheng Wang, Guan Quan, Paul Shepherd

Research output: Contribution to journalArticlepeer-review

8 Citations (SciVal)
15 Downloads (Pure)


Grid shells have been widely used in various long-span public buildings, and many of them are defined over free-form surfaces with complex boundaries. This emphasizes the importance of general and digitalised grid generation and optimization methods in the initial design stage to achieve visually sound grid shells. In this paper, a framework is presented for the development of a digital tool and to generate regular and fluent grids for structural design over free-form surfaces, especially those with complex boundaries. Both triangular and quadrilateral grid generation are addressed. To generate regular and fluent grids for free-form surfaces, a simple yet practical framework is proposed based on a spring-mass model. Firstly, an initial casual quadrilateral grid is tiled on the surface based on surface discretization and mesh parameterization. Secondly, the distribution of the initial grid vertices is adjusted by a dynamic relaxation procedure, assuming the grid as a spring-mass system. Thirdly, the grid vertices corresponding to the adjusted particles in the equilibrium state are then reconnected to produce a grid with a predefined pattern (triangular or quadrilateral). Finally, the generated grid is relaxed with the spring-mass model, alongside additional geometric operations including grid size adjustment and filtering techniques, to further improve the grid regularity and fluency. As part of its contribution, this paper also broadens the application scope of the fluency index, which can be used to quantitatively evaluate the suitability of a given triangular or quadrilateral grid for architectural and structural expression. Examples are presented and show that the proposed framework is effective for the triangular and quadrilateral grid generation over various surfaces and to optimize the resulted grids along complex boundaries. The method proposed can be useful for rapid design and performance evaluation of free-form grid structures.

Original languageEnglish
Article number104025
JournalAutomation in Construction
Early online date26 Oct 2021
Publication statusPublished - 31 Jan 2022

Bibliographical note

Funding Information:
This research was sponsored by the National Natural Science Foundation of China under Grant 51678521 , 51778558 and by the Natural Science Foundation of Zhejiang Province LY15E080017 . The project is also supported by the Foundation of Zhejiang Provincial Key Laboratory of Space Structures, Grant 21705. The authors would like to thank them for their financial support.


  • Dynamic relaxation
  • Free-form surface
  • Grid quality
  • Grid structure
  • Parametric design

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Civil and Structural Engineering
  • Building and Construction


Dive into the research topics of 'Digital and automatic design of free-form single-layer grid structures'. Together they form a unique fingerprint.

Cite this