Degenerate tetrahedra removal

Standard 3D mesh generation algorithms may produce a low quality tetrahedral mesh, i.e., a mesh where the tetrahedra have very small dihedral angles. In this paper, we propose a series of operations to recover these badly-shaped tetrahedra. In particular, we will focus on the shape of these undesired mesh elements by proposing a novel method to distinguish and classify them. For each of these configurations, we apply a suitable sequence of operations to get a higher mesh quality. Finally, we employ a random algorithm to avoid locks and loops in the procedure. The reliability of the proposed mesh optimization algorithm is numerically proved with several examples.