Computational Grid Generation on the Design of Freeform Shells with Complex Boundary Conditions

The free-form grid structures have been widely used in various public buildings, and many of them are trimmed with complex curves including internal voids. Computational design software enables the rapid conceptual creation of such complex surface geometry, whereas it is neither a convenient nor an obvious task for engineers to create a discrete grid structure on a free-form surface with complex boundary conditions that manifest the designer’s intension. This emphasizes the importance of grid generation tools and methods in the initial design stage. This paper presents an efficient design tool for the synthesis of free-form grid structures based on the “guide line” and surface flattening methods, considering complex features of internal boundaries on trimmed free-form surface. The method employs a fast and straightforward approach which achieves grids with rods of balanced length and fluent lines. In order to generate grids on the trimmed free-form surface with complex boundaries, the grid generation method which combines surface flattening and improved guide line method is put forward. The data of trimmed surface includes a complete surface and the trimming curves. The parametric domain of the complete NURBS surface was firstly divided into a number of parts and a discrete free-form surface was accordingly formed by mapping dividing points onto surface. The free-form surface was then flattened based on the principle of identical area. Accordingly, the flattened rectangular lattices were fitted into the 2D surface where grids were formed applying the guide line method. Subsequently, the intersections of guide lines and the complex boundary were obtained and the guide lines were modified and divided equally to get grids by connecting dividing points. Finally, the 2D grids were mapped onto the 3D surface to achieve grid on free-form surface with complex boundaries. A spring-mass method was also employed to further improve the smoothness of the resulted grids. Examples were presented to shown the effectiveness of the proposed method.