Research And Implementation Of Grid Meshing Method For Free-form Grid Structures

With the development of computer aided technology,as well as the improvement of architectural modeling art and the transformation of people's aesthetic standard,free-form spatial structures appear in the public's views more and more frequently,these free-form surface structures have flexible designed shape,which can reflect outstanding visual expression and satisfy abundant architectural demand,that's why they are applied to public landmark by architectures and structural engineers increasingly.However,it's hard to find an appropriate grid meshing method for free-form spatial structures to ensure the uniform sizes,the same links and the fluent lines,because the shapes of the surfaces are special and changeable,the current study on grid generation of free-form grid structures is still in primary stage,there exists no widely accepted theory and method of grid generation.Based on above,the article provides three ideas or methods on grid generation:Aiming at the double parameterized mechanism of NURBS surface,a method based on mapping theory and adjustment technique is proposed.Divide the boundary of free-form surface with the given length,the given segments,the given ratio or the given lengths,the divided boundary points are mapped back to the parametric domain,connect any two boundary points in the parametric domain to generate a straight line,then map these straight lines onto free-from surface to obtain curves,the curves can accord with move towards of the surface well,as well as smooth and uniform spacing distance.These curves can be modified by adding control points to the straight lines in parametric domain,so as to adjust the curves better.Quadrangular grids can be generated by intersection of two directional curves,and triangular grids can be generated by curve-advancing method,that is,divide each curve in order,then connect links between adjacent curves with best topology.In conclusion,the method innovates in curves generating and grids advancing,and the grids generated have advantages of fluent lines and uniform sizes in most situations.Aiming at some surfaces with irregular shape,a method based on surface partition is proposed.Based on the interpolation fitting theory of NURBS surface,we sort the target surface into simple divided surface and complex divided surface,for both of them we try to construct rectangular lattices of N×M to fit a new surface.Once the surface is divided,the method based on mapping theory can be adopted.The result shows that the method can generate fine grids,especially on some special free surfaces,and it will be a good supplement to the former method.Considering that plane is easier to generate grids than surface,a method based on surface flattening and mapping theory is proposed.Divide the parametric domain of free form surface into the given number in both directions,and map these discrete points 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,that is,regarding the diagonal line on the free-form surface as the base line,the surface is then flatted starting from the center point,from inside to outside,based on the rule of minimum area variation,the flattening method provided can reflect the shape,trend and area distribution of free-form surface well.The flatted rectangular lattices will be fitted into a 2D surface next,then divide the 2D surface into 6 parts from the center point with the same angle,considering the different boundary conditions,the line advancing method is adopted to generate triangular grids for each part,so grid generation is realized for the whole 2D surface eventually.The 2D grids are mapped back to the free form surface based on the constant topology.The method proposed will give consideration to both uniformity and fluency,able to get to equilibrium between them.In conclusion,this article explores grid meshing on free-form grid structures from three different aspects,the progress we get will provide reference and theoretical support for grid designing of free-form surfaces.