Research On Hexagonal Mesh Generation Method Based On Quadrilateral Mesh

With the continuous development of computer technology today,discrete graphics techniques are gaining more and more attention.Among them,triangular mesh and quadrilateral mesh have been widely researched and applied in rendering,modeling and analysis,but in some specific structure of materials,such model representation is still not accurate enough,and hexagonal mesh which can precisely model some materials,stably and beautifully as well as has the prospect of wide application is only less researched.In order to generate hexagonal mesh and study it,this paper borrows the existing mature quadrilateral mesh to generate hexagonal mesh,and proposes a field-guided method in order to solve the problem of adding user’s freedom in mesh generation and making the generated surface closer to the regular hexagon.Finally,this paper analyzes and explores the two algorithms and the corresponding generated hexagonal mesh.The main work accomplished in this paper is as follows.(1)Generating hexagonal mesh based on splitting method.By analyzing the quadrilateral mesh,in order to achieve a concise,efficient and robust algorithm,while considering a good treatment of singularities,this paper proposes a split-based approach to generate hexagonal mesh.(2)Generating hexagonal mesh based on field guidance method.The 6-valued triangular mesh is generated by using the guidance of directional and position fields,which is essentially a smoothing of the defined quotient space and thus generates a hexagonal mesh.The method combines local parameterization and global control to achieve global optimality.In this paper,the establishment of the hierarchy is improved and the optimal results are calculated using a random GS iterative method.This method adds the user control over the edge lengths with the generated mesh,and makes the faces of the mesh closer to the regular hexagon while leaving the quadrilateral mesh dependence.(3)Algorithm and mesh analysis.The geometric properties of the generated mesh are evaluated by the comparative analysis of the generated mesh and the original quadrilateral mesh,the theoretical analysis and actual measurement of the Hausdorff distance,and the theoretical analysis of the algorithm.The computational efficiency of the two algorithms is understood through theoretical analysis and experimental statistics on the time complexity of the algorithms.The mechanical properties of the hexagonal mesh are evaluated by simulation experiments on the hexagonal mesh and the quadrilateral mesh.The final experimental analysis shows that the Hausdorff distances of the two algorithms do not exceed twice the longest edge length and the user-specified edge length,respectively,which ensures the geometric features of the graph,and through further exploration,it is found that the split-based method for generating hexagonal mesh is a technique for generating quadrilateral mesh into a dual hexagonal mesh of equal resolution,while the field-guided method for generating hexagonal mesh,on the other hand,generates a mesh with different geometric properties due to the different ways of energy smoothing.Concerning the computational efficiency,two algorithms are computationally efficient,and the actual computational time statistics under their general graphics show that they are completed within seconds,and the split-based algorithm for generating hexagonal mesh is even less than 1 second.At the same time,under the same resolution,the hexagonal mesh has a more uniform force,more overall deformation,and roughly 2-5 times the deformation size of the quadrilateral mesh.In addition,the structure is more likely to absorb and store energy,which has good prospects for application.