Computational grid generation for the design of free-form shells with complex boundary conditions

Tierui Li, Jun Ye, Paul Shepherd, Hui Wu, Boqing Gao

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10 Citations (SciVal)
158 Downloads (Pure)


Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifests the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on guideline and surface-flattening methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete nonuniform rational basis spline (NURBS) surface is first divided into a number of patches, and a discrete free-form surface is formed by mapping dividing points onto the surface. The free-form surface is then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the two-dimensional (2D) surface, with grids formed by applying a guideline method. Subsequently, the intersections of the guidelines and the complex boundary are obtained, and the guidelines are divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the three-dimensional (3D) surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes by presenting realistic examples to demonstrate the practical effectiveness of the proposed method.

Original languageEnglish
Article number000828
JournalJournal of Computing in Civil Engineering
Issue number3
Early online date29 Jan 2019
Publication statusPublished - 31 May 2019


  • Complex boundary
  • Free-form gridshell
  • Grid generation
  • Grid relaxation
  • Guideline method
  • Surface flattening

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Computer Science Applications


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