The Study And Application Of Tetrahedral Mesh Generation Method Based On Surface Model

The research on mesh generation technology is a method which is to divide thecontinuous computational region into simple and discrete geometrical elements. Meshgeneration technology has been used to analyze the finite elements since last century.With the development of the information technology and the improvement of computertechnology，it has been widely applied into the fields of geographic information system,Computational fluid dynamics, computational visualization and computer graphic etc.And it has become one of the important research objects in the field of computationalgeometry. Nowadays, many fine and stable algorithms for triangular mesh generationhave emerged in2-D plane region. While in3-D spatial region, the optimized criterionfor triangulation in2-D can’t be totally extended in3-D occasion. And the process ofthe boundary elements for tetrahedral mesh generation still has been a difficulty. Allthese problems have brought some challenges and opportunities for the continuousdevelopment of triangulation in3-D region. Therefore, the research aimed at thetriangular mesh generation in3-D space has the significant meaning and realistic value.In terms of the different expression form of the surface model, the tetrahedral meshgeneration algorithm based on surface can be divided into two different processes underexplicit and implicit condition. Delaunay triangulation and advancing front algorithmare the most representative methods under explicit condition. These methods operatearound the surface model and focus the energy on the confirmation of the current frontand the recover of original surface. The method based on spring oscillator is a commonapproach under implicit condition. This method can achieve an optimal mesh by solvingthe balanced status of each node, which ensures the conformation of the boundary.While, the boundary expressed by distance function is too simple at present and theapplication is limited in scope. And the surface model can be approximated by fittedelement whose computational process is complex.For the expression of boundary, a method which can convert the surface triangularmodel into boundary indicator function is given in this paper. First, a geometric methodis applied to reconstruct a classified volume data of specified size from the triangularsurface model in this method, and a balanced octree based on the giving surface model is built to compute a3-D array which is used to control the mesh size. Then, the volumedata is converted into a boundary indicator array in which different isosurfaces areconformed in the neighborhood.After the research and the comparison of the existing tetrahedral methods underexplicit and implicit condition, the weakness of restraining sliver in spring oscillatorbased method is improved. A new self-organized algorithm for generation of tetrahedralmesh is introduced by combining our improved self-organized algorithm with theinterpolation function of related3-D data. The experimental result shows that thismethod can be used to generate high quality tetrahedral mesh at higher proportion andensure the conformation of the boundary additionally.