Grid generation on free-form surface using guide line advancing and surface flattening method

Automatic grid generation on a curved surface is important to more efficient design of free-form structures. However, it is neither a convenient nor an obvious task for engineers to create a discrete grid structure on a complex surface that meets the architectural requirements. Besides, research on the rapid grid generation methodology for free form structural design is still limited. In order to achieve better grid distribution of rods on free-form 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. A grid shape and rod length quality index was proposed to evaluate the shape of grid cells and rod lengths. The results show that the grid shape quality index and the deviation of rod length of the grid structure are reduced by up to 47% and 34% respectively by using the guide line method with surface flattening when compared to the method without surface flattening.