Architectural Grid Generation And Multiobjective Control For Complex Free Form Surfaces

With improvements in design theory,computer-aided design and construction technology,more and more free-form grid structures have appeared around the world.These structures have fanciful shapes and strong visual expression,and are gaining increasing popularity among architects and the public.However,there is currently no mature and widely applicable meshing method and corresponding software yet.Therefore,it is of great theoretical significance and application value to study how to efficiently generate meshes that meet architectural requirements over complex surfaces for grid structures.This article systematically studies this topic,and proposes a series of effective meshing and control methods to deal with the potential needs of architectural grid design,including the adaptation of complex surfaces,the grid control of size,trend and topology,surface feature retention,etc.The details are as follows:A new triangular mesh generation method for the free-form curved surfaces is developed based on the mapping technique and the truss-like method,and thus name the mapping truss-like method.With explicit control on mesh size by the desired relative length function,this method can generate uniform meshes or adaptive meshes in harmony with the surface features for various free-form surfaces.Another automatic triangular mesh generation method is presented,based on bubble dynamics simulation and a modified Delaunay method,and thus named spacial bubble-like method.In this method,grid nodes are regarded as elastic bubbles and their equilibrium positions are solved directly in space.Thus,this method overcomes the mapping distortion problem in the mapping truss-like method and improves the mesh quality.The control of the grid size is realized by the relative radius function.The resulting grids have regular shapes and adaptive sizes.Based on the spatial bubble method for generating uniform meshes,a topology optimization algorithm aiming at improving grid regularity is introduced.Combined with the mesh relaxation method based on spring net simulation,a triangular mesh generation and optimization system is proposed.A new index is proposed and included in the system to evaluate the grid fluency.The final meshes created by the system are uniform,well-shaped and fluentTo better express the architectural implication,a grid generation method is presented by offsetting the guide curve on the surface directly,called spatial guide curve method.The grid trend is controlled by the guide curve,and the grid shape is optimized by merging offset points which are too close.The meshes generated by this method have advantages of regular shapes,fluent lines and desired trend,and a disadvantage of poor meshes near the boundary.To better accommodate the boundary,a new method named mapping equal-division method is proposed based on the mapping technique and bidirectional equal-division of curves.Specific operations to specific surfaces are added to this method to extend its application scope and improve the grid quality.The resulting grids are featured by uniform sizes,fluent lines and various patterns.Based on the mapping equal-division method,an adaptive grid generation method is proposed for complex multiple surfaces.The grid size can be adaptive to boundary conditions or surface shapes by adjusting the rules of curve dividing.The resulting grids have fluent lines,regular shapes and various patterns.This article proposes a variety of meshing methods to achieve deep control of grid size,orientation and topology.However,given the diversity of architectural grid requirements,it is difficult to have a meshing method that achieves satisfactory results under different conditions.Hence,the above methods are finally integrated into a system for the design of free-form meshes.The system provides a highly efficient,flexible and powerful tool to design grids interactively,which can meet the requirements of the architectural grids to a large extent.