No abstract

No abstract

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 manifest the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on "guide line" 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 NURBS (Non-Uniform Rational B-Spline) surface is firstly divided into a number of patches, and a discrete free-form surface formed by mapping dividing points onto the surface. The free-form surface was then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the 2D surface, with grids formed by applying a guide-line method. Subsequently, the intersections of the guide-lines and the complex boundary are obtained, and the guide-lines divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the 3D surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes bypresenting realistic examples to demonstrate the practical effectiveness of the proposed method.

No abstract