Grid generation on free-form surface based on surface flattening

A method based on surface flattening and mapping theory was proposed in order to realize grid generation on free-form surface. The parametric domain of free-form surface was divided into the given number in both directions, and these discrete points were mapped back to free-form surface so as to generate rectangular lattices on the surface. Surface flattening can be realized by making efforts to flat the rectangular lattices. The diagonal line on the free-form surface was regarded as the base line. The surface was flatted starting from the center point, from inside to outside, based on the rule of minimum area variation. The provided flattening method can reflect the shape, trend and area distribution of free-form surface well. Then the flatted rectangular lattices were fitted into a two-dimensional surface. The two-dimensional surface was divided into 6 parts from the center point with the same angle. Considering the different boundary conditions, the line advancing method was adopted to generate triangular grids for each part. Grid generation was realized for the whole two-dimensional surface. The two-dimensional grids were mapped back to the free form surface based on the constant topology. The proposed method can apply to many different cases, and the grids generated by the method have advantages of fluent lines and uniform sizes. © 2016, Zhejiang University Press. All right reserved.