HybridOctree_Hex: Hybrid Octree-Based Adaptive All-Hexahedral Mesh Generation with Jacobian Control

We present a new software package, "HybridOctree_Hex," for adaptive all-hexahedral mesh generation based on hybrid octree and quality improvement with Jacobian control. The proposed HybridOctree_Hex begins by detecting curvatures and narrow regions of the input boundary to identify key surface features and initialize an octree structure. Subsequently, a strongly balanced octree is constructed using the balancing and pairing rules. Inspired by our earlier preliminary hybrid octree-based work, templates are designed to guarantee an all-hexahedral dual mesh generation directly from the strongly balanced octree. With these pre-defined templates, the sophisticated hybrid octree construction step is skipped to achieve an efficient implementation. After that, elements outside and around the boundary are removed to create a core mesh. The boundary points of the core mesh are connected to their corresponding closest points on the surface to fill the buffer zone and build the final mesh. Coupled with smart Laplacian smoothing, HybridOctree_Hex takes advantage of a delicate optimization-based quality improvement method considering geometric fitting, Jacobian and scaled Jacobian, to achieve a minimum scaled Jacobian that is higher than $0.5$. We empirically verify the robustness and efficiency of our method by running the HybridOctree_Hex software on dozens of complex 3D models without any manual intervention or parameter adjustment. We provide the HybridOctree_Hex source code, along with comprehensive results encompassing the input and output files and statistical data in the following repository: https://github.com/CMU-CBML/HybridOctree_Hex.