Error-bounded Edge-based Remeshing of High-order Tetrahedral Meshes

Abstract

We present a robust method to generate high-quality high-order tetrahedral meshes with bounded approximation errors and low mesh complexity. The success of our method relies on two key components. The first one is three novel local operations that robustly modify the topology of the high-order tetrahedral mesh while avoiding invalid (flipped or degenerate) elements. In practice, our meshing algorithm follows the edge-based remeshing algorithm that iteratively conducts these local topological operations and a geometric optimization operation to improve mesh quality. The second is a new containment check procedure that robustly judges whether the approximation error between the input mesh and the high-order mesh exceeds the user-specified bound. If one operation causes the error-bounded constraint to be violated, we reject this operation to ensure a bounded approximation error. Besides, the number of tetrahedrons of the high-order mesh is reduced by progressively increasing the target edge length in the edge-based remeshing algorithm. A large number of experimental results have shown the capability and feasibility of our method. Compared to other state-of-the-art methods, our method achieves higher robustness and quality.