Design And Implementation Of A New Tetrahedron Subdivision Based On Triangular Grid

The tetrahedron subdivision algorithm has important application value in many fields such as finite element analysis,computational fluid dynamics,scientific computation visualization,robotics and biomedicine.In this paper,the common algorithms for generating tetrahedral meshes are studied and compared.The principles,advantages and disadvantages of Octree,Advancing Front Method,Delaunay are mainly analyzed and discussed.Based on the proposed new tetrahedron subdivision constraints,this paper inherits the excellent features of traditional algorithms and makes some improvements to the defects.It aims to generate a tetrahedral mesh that satisfies the finite element analysis,and studies how to use a fully automatic method to generate efficiently and highly reliable tetrahedral meshes.The main research content is:Based on the computational geometry of tetrahedral meshing,this paper does a lot of research on the current mainstream tetrahedral mesh generation algorithms,and outlines the basic principles,basic ideas and algorithms of Octree,Advancing Front Method and Delaunay methods.And the characteristics and deficiencies of the three algorithms were compared and analyzed.The new tetrahedron subdivision constraints proposed in this paper solves the basis and core problem of the tetrahedral subdivision algorithm for the current candidate plane to select an optimal candidate point from the candidate point set,and inherits the excellent characteristics of mainstream tetrahedron subdivision.Such as the reliability of the algorithm theory,strong adaptability,high efficiency of splitting,and stable results of subdivision,and it also largely avoids the complicated point,line,surface and four-face neighboring relationships in the three-dimensional dissection field.Excessive addition of Steiner points occurs,and the number of singular tetrahedral elements is reduced.Only a small number of singular elements appear in the boundary area at the end of the split.Based on the proposed new tetrahedron subdivision constraints,this paper analyzes and designs the tetrahedron subdivision algorithm as a whole,and selects and designs highly adaptable methods such as closed inspection,normal vector inspection,subdivision direction limitation,and unit crossover inspection.For the proposed new tetrahedron subdivision criteria,a reasonable and effective data structure is designed for the data set,which is used to efficiently extract the connection data between points,lines,triangles,and tetrahedrons when generating a new tetrahedron element,which allows the program to meet the needs of tetrahedron subdivision.Based on the above technical research,the tetrahedral mesh generation was implemented using C/C++,and many tetrahedral meshing problems in engineering applications were successfully solved.The research results show that the new algorithm based on the new tetrahedron subdivision is robust,effective and efficient,and the mesh generated is high quality and easy to implement.