Study On Theory And Methods Of Grid And Surface Generation With Boundary Constraints

Based on the study about the theories and methods of grid and surface generation with boundary constrains, several methods of grid and convolution surface were presented and discussed.A method based on boundary deformation for grid generation was presented. Firstly, the initial grid was generated by the four corners of the boundary lines. Then the deformation matrix, between the initial grid and the target grid, could be calculated recursively according to the boundary lines. Finally, the target grid in the domain with boundary constrains generated. The grid was generated very fast by using this method, and there are no such unusual wave curves generated by those optimization methods which using the grid nodes as variables. For the problem of generating poor quality grids on some complex boundary zone by this method, it can be resolved by redefining the boundary.We proposed a stress balance method to generate elastic grid, where the grid nodes was easy to obtain by solving the iterate equations. For there does stable equilibrium position in the cell for compression deformation in one direction at least, we improved the equilibrium equation by using logarithmic function. Then, there must be an equilibrium position which can be quickly reached in the cells, except those completely compression in two directions. Moreover, in practice, for the complexity of boundary shape, there may exist completely compression cells in zone. It was recommended to set the entire zone as tensile deformation, and the formula of parameter setting was proposed. Numerical experiments showed that the grids generated by (improved) stress balance method meet the physical characteristics of the denser grid curves near the concave boundary and the sparser grid curves near the convex boundary.A method to generate the grid by the curve clusters with shape parameters in two directions was proposed. The following theorem ensured that the method can also be used in space grid generation. Then, the influence of shape parameters on the grids was discussed by considering a variety of different shape boundaries. Based on the theorem about the relative positions of the adjacent grid curves, an objective function to solve the optimal shape parameters was constructed. Numerical experiments showed that the grid generated by the method and the objective function owns the same density characteristics of the curves. More importantly, the grid generated by the method was shape-controllable.By using the exponential function, a method to generate density controllable grid is presented. Then we discussed the influence of density parameters on generating the grids with all kinds of shape boundaries. Based on the measurements of cells, a square criteria to obtain the optimal density parameters was proposed. Numerical experiments showed that the optimal grid was significant better than the general, when there exists some difference between the boundary in two direction.The two methods with parameters listed above both owned the characteristics of the lower algorithm space and the lower algorithm complexity for there only existing two optimal variables in objective functions. Moreover, the methods were easy to converge.The method to generate the convolution surface constrained with contour curves was discussed. First, a brief introduction of implicit surface modeling based on the metaball. In this method, the contour curves was approximated by the ball or ellipse, and the surface was constructed by the extended metaball model which using the hyper-quadratic as the primitive. Then a modeling method of convolution surface was proposed. In this method, a two-dimensional surface shape formed by inward offset lines of the contour curves was used as the skeleton to construct the surface, which met the condition of approximating the given contour curves. Finally, we introduced two methods to generate the offset lines of the contour curves, and then derived the analytical formula of field value and analyzed its error. Experiments showed that our methods were especially used to generate flat model.