ABSTRACT
The rapid development of finite element simulations in computational medicine, biology, material sciences and engineering has increased the need for quality mesh generation. This chapter reviews unstructured triangular and tetrahedral mesh generation. It introduces octree-based mesh generation techniques from scanned images, their extension to multiple-material domains, how to resolve topology ambiguities and improve the mesh quality, and dual contouring-based mesh generation with guaranteed angle range. There are three main methods for triangular and tetrahedral mesh generation: octree-based methods, Delaunay triangulation and advancing front methods. The octree-based methods generally create a new mesh for the input boundary. Delaunay triangulations maximize the minimum angle of the triangulation, tending to avoid “sliver” triangles. According to the Delaunay criterion, Delaunay triangulation maximizes the minimum angle, and any circumcircle does not contain any other input points in its interior. The most straightforward way to implement Delaunay triangulation is to repeatedly insert one vertex at a time and retriangulate the affected elements surrounding that vertex.
