Improved Boundary Constrained Tetrahedral Mesh Generation by Shell Transformation

Summary An excessive number of Steiner points may be inserted during the process of boundary recovery for constrained tetrahedral mesh generation, and these Steiner points are harmful in some circumstances. In this study, a new flip named shell transformation is proposed to reduce the usage of Steiner points in boundary recovery and thus to improve the performance of boundary recovery in terms of robustness, efficiency and element quality. Shell transformation searches for a local optimal mesh among multiple choices. Meanwhile, its recursive callings can perform flips on a much larger element set than a single flip, thereby leading the way to a better local optimum solution. By employing shell transformation properly, a mesh that intersects predefined constraints intensively can be transformed to another one with much fewer intersections, thus remarkably reducing the occasions of Steiner point insertion. Besides, shell transformation can be used to remove existing Steiner points by flipping the mesh aggressively. Meshing examples for various industrial applications and surface inputs mainly composed of stretched triangles are presented to illustrate how the improved algorithm works on difficult boundary constrained meshing tasks.