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Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

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

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions Thumbnail


Boqing Gao

Hui Wu

Paul Shepherd

Tierui Li

Jun Ye


© 2019 American Society of Civil Engineers. 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.


Gao, B., Wu, H., Shepherd, P., Li, T., & Ye, J. (2019). Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions. Journal of Computing in Civil Engineering, 33(3), 4-17.

Journal Article Type Article
Acceptance Date Sep 25, 2018
Online Publication Date Jan 29, 2019
Publication Date May 1, 2019
Deposit Date Mar 21, 2019
Publicly Available Date Mar 21, 2019
Journal Journal of Computing in Civil Engineering
Print ISSN 0887-3801
Publisher American Society of Civil Engineers
Peer Reviewed Peer Reviewed
Volume 33
Issue 3
Pages 4-17
Keywords free-form gridshell, complex boundary, surface flattening, guide-line method, grid generation,
grid relaxation
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