Hexahedral Meshing Based On Global Parameterization

With the rapid development of computer graphics and hardware technology,three-dimensional technology is gradually being used to represent various three-dimensional entities,such as discrete point clouds,grids,and so on.More and more people are interested in the study of three-dimensional models.The finite element method is an important part of mathematical calculations.It mainly includes slice interpolation and discretization,that is,using a grid to represent objects.At the same time,grid technology has gradually become an important field of research,and many aspects such as finite element analysis,biomedicine and graphics have their wide applications.Grid technology includes tetrahedral mesh generation technology and hexahedral mesh generation technology.Compared with tetrahedral mesh,hexahedral mesh has advantages in anti-distortion.In the past few years,many algorithms for generating hexahedral meshes have been proposed.However,it has not yet achieved the effect of satisfying both high quality and automatic adaptation to any complex topology.So an important conclusion is that generating a full hexahedral mesh on any area is still impossible.Therefore,a dominant hexahedral mesh has been proposed.Compared with a full hexahedral mesh,the dominant hexahedral mesh allows the hexahedron,prism,vertebral body and tetrahedron to be aggregated.The goal is to create a dominant hexahedral element in the grid,including the number of vertices and volume.We propose a new dominant hexahedral mesh generation algorithm,while input a tetrahedral mesh,the new mesh is created which most of the cells is a hexahedron.Our strategy consists of three steps: the first step is to create a frame field to control the position and orientation of the cell.The second step is to generate a point set,most of which correspond to the vertices on the frame field.We choose a periodic global parameterization algorithm.In the two-dimensional,although the algorithm can not generate all hexahedrons in the volume,it can produce hexahedrons within the volume that conform to the desired stretch and direction,and there is no constraint on the frame field.The resulting mesh is a dominant hexahedral mesh.The mesh cells are not all hexahedral meshes,which produce some non-hexahedral elements at the singular points generated by the periodic global parameterization algorithm.In the third step,tetrahedrons are obtained by the point set Delaunay triangulation algorithm,and tetrahedrons are merged to create a hexahedron.We perform extended analysis based on the Meshkat algorithm,enumerating all possible configurations and understanding all possible split structures: any split cube can be simply described as a six-atom configuration.This special understanding makes the algorithm shorter,more efficient,and easier to implement.Finally,this paper selects several sets of 3D models for hexahedral mesh reconstruction,which is compared with the Carrier algorithm.In the case of the similar number of hexahedral vertices,the number of hexahedrons and the volume of the hexahedron are larger.It proves the good feasibility and efficiency of the proposed algorithm.