HexDom: Polycube-Based Hexahedral-Dominant Mesh Generation

Abstract

In this paper, we extend our earlier polycube-based all-hexahedral mesh generation method to hexahedral-dominant mesh generation, and present the Hex-Dom software package. Given the boundary representation of a solid model, Hex-Dom creates a hex-dominant mesh by using a semi-automated polycube-based mesh generation method. The resulting hexahedral dominant mesh includes hexahedra, tetrahedra, and triangular prisms. By adding non-hexahedral elements, we are able to generate better quality hexahedral elements than in all-hexahedral meshes. We explain the underlying algorithms in four modules including segmentation, polycube construction, hex-dominant mesh generation and quality improvement, and use a rockerarm model to explain how to run the software. We also apply our software to a number of other complex models to test their robustness. The software package and all tested models are availabe in github (https://github.com/CMU-CBML/HexDom).

Hex-Mesh Generation and Processing: a Survey

“…However, local surface orientation often does not produce a globally consistent structure, and heuristic post-processing is necessary to fix the labeling. Hu and Zhang [2016] use a modified CVT labeling in the space of normals, but still require manual post-processing to sanitize topological inconsistencies that may arise [Yu et al 2021[Yu et al , 2020. The authors of PolyCut [Livesu et al 2013] listed sufficient topological conditions for the existence of a valid polycube (following [Eppstein and Mumford 2010]) and -starting from naive labeling -systematically explore the space of labelings in order to find the closest label assignment that satisfies all such criteria.…”

“…Also this method is not guaranteed to converge to a valid polycube structure. Interactive tools for user assisted polycube construction also exist [Li et al 2021;Yu et al 2021Yu et al , 2020.…”

“…Similarly to LoopyCuts , HexDom [Yu et al 2021] produce a block decomposition where each block is either hex, prism, or tetrahedral cell. This method extends the approach for polycube generation proposed in [Hu and Zhang 2016] based Voronoi tessellation (CVT) to include non-hex elements.…”

“…Since these tools follow a divide-and-conquer approach, direct hexmeshing techniques are preferred to indirect ones, because they ensure that the meshes of all sub components will be conforming. In recent years, academic literature has started to explore the possibility to couple user guidance with indirect approaches that operate on a supporting tetrahedral mesh [Li et al 2021;Takayama 2019;Yu et al 2021Yu et al , 2020. These methods are not based on the typical divide-and-conquer paradigm, and their ability to scale on complex shapes it yet to be demonstrated.…”