A Novel Geometric Flow-Driven Approach for Quality Improvement of Segmented Tetrahedral Meshes

This paper presents an efficient and novel geometric flow-driven method for mesh optimization of segmented tetrahedral meshes with non-manifold boundary surfaces. The presented method is composed of geometric optimization and topological transformation techniques, so that both location and topology of vertices are optimized. Non-manifold boundary can be divided into manifold surface patches having common boundary curves with each other. We adopt the averaged curvature flow to fair boundary curves with shape preserved, and the averaged mean curvature flow to fair surface patches with the property of volume-preserving. Meanwhile, boundary meshes are regularized by adjusting curve nodes and surface nodes along tangent directions. Locations of interior nodes are optimized by minimizing an energy functional which reflects the mesh quality. In addition, face-swapping and edge-removal operations are applied to eliminate poorly-shaped elements. Finally, we validate the presented method on several application examples, and the results demonstrate that mesh quality is improved significantly.