Research On Grid Meshing Method For Free-form Grid Structures

In recent years, traditional spatial structural shapes including plane, cylindrical surface,spherical surface, and parabolic surface have not met people’s aesthetic needs of the architectural appearance. At the same time, with the development of construction industry and advances in computer aided geometric techniques, the free-form spatial grid structures with rich expression are more and more popular with architects and structural engineers. Although free-form surface brings us good visual effects, traditional meshing method isn’t appropriate for this type of surface because the shape of the surface is novel and changeable. Therefore,how to generator smooth and beautiful mesh on this kind of surface is the key of implementation of free-form grid structures. Based on this subject, a preliminary study on grid generation of three kinds of free-form surface is performed in this paper.For the complete surface, a grid generation methodology which combines surface flattening technique with guide line method is put forward. The parametric domain of the free-form surface was firstly divided into a number of parts and a discrete free-form surface was accordingly formed by mapping the generated dividing points onto the curved 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 by using the guide line method. Finally, the 2D grids were mapped onto the 3D surface, and grids were therefore generated on the given surface. The results show that this method can not only generate grids that meet the requirements of regular shape and fluent lines, but also control the trends of free-form surface grids.For the free-form surface with inner boundary, this paper firstly flattens surface, and then the improved guide line method is adopted. Accordingly, the intersections of guide lines and the inner boundary are found and the guide lines are corrected. Finally, the 2D grids are mapped onto the 3D surface, so as to achieve the goal of grid generation on free-form surface with inner boundary. The guide line method is generalized for grid generation on the free-form surface with inner boundary and grids around the inner boundary are high quality.For the trimmed free-form surface with complex boundary shape that needs the better meshing methods and skills, this paper firstly classifies trimmed free-form surfaces, and then surface flattening and improved guide line method are used for generating grids on each type of trimmed surface. This method implements grid generation on all types of free-form surface with complex boundary.In short, this paper studies on grid generation of three kinds of free-form surface and hopes to provide reference and technical support for the design of free-form grid structures.