Reliable Isotropic Tetrahedral Mesh Generation Based on an Advancing Front Method

In this paper, we propose a robust isotropic tetrahedral mesh generation method. An advancing front method is employed to control local mesh density and to easily preserve the original connectivity of boundary surfaces. Tetrahedra are created by each layer. Instead of preparing a background mesh for mesh spacing control, this information is estimated at the beginning of each layer at each node from the area of connecting triangles on the front and a user-specified stretching factor. An alternating digital tree (ADT) is prepared to correct the mesh spacing information and to perform geometric search efficiently. At the end of the mesh generation process, angle-based smoothing and Delaunay refinement are employed to enhance the resulting mesh quality. Surface meshes are prepared beforehand using a direct advancing front method for discrete surfaces extracted from computed tomography (CT) or magnetic resonance imaging (MRI) data. The algorithm is demonstrated with several biomedical models.