Feature Preserving Octree‐Based Hexahedral Meshing

Abstract

We propose an octree‐based algorithm to tessellate the interior of a closed surface with hexahedral cells. The generated hexahedral mesh (1) explicitly preserves sharp features of the original input, (2) has a maximal, user‐controlled distance deviation from the input surface, (3) is composed of elements with only positive scaled jacobians (measured by the eight corners of a hex [SEK*07]), and (4) does not have self‐intersections. We attempt to achieve these goals by proposing a novel pipeline to create an initial pure hexahedral mesh from an octree structure, taking advantage of recent developments in the generation of locally injective 3D parametrizations to warp the octree boundary to conform to the input surface. Sharp features in the input are bijectively mapped to poly‐lines in the output and preserved by the deformation, which takes advantage of a scaffold mesh to prevent local and global intersections. The robustness of our technique is experimentally validated by batch processing a large collection of organic and CAD models, without any manual cleanup or parameter tuning. All results including mesh data and statistics in the paper are provided in the additional material. The open‐source implementation will be made available online to foster further research in this direction.

Hex Me If You Can

“…Gmsh [7] does not mesh only the volume, but also the feature entities as defined by the CAD model. In addition to the tetrahedral cells, there are triangular, edge and vertex cells 4 to respectively discretize feature surfaces, curves and points. Those features are identified by the CAD with a color (i.e.…”

“…3 ∼ 5 citations per week 4 those lower dimensional cells are conforming to the higher ones There are then 189 meshes, whose the given filenames (s|n|i)(\d{2})(c|u|b) {extra}.vtk summarize the corresponding model (s|n|i)(\d{2}) and mesh (c|u|b) types.…”

“…Automatic methods such as advanced frontal [2] and polycubebased [3] approaches are not guaranteed to be robust, neither to build high quality hexahedra. Solely octreebased procedures [4] can automatically and robustly supply a full hexahedral mesh, but with a quality far from ideal on the boundary. Three-dimensional octahedral frame-based methods are able to automatically and robustly make a high quality mesh, provided that the octahedral singularities (i.e.…”

3D-TSV: The 3D Trajectory-based Stress Visualizer

“…A finite-element-based elasticity analysis has been used to compute the stress field for each model under the predicted loads. The unstructured hexahedral meshes 'BunnyHex' and 'KittenHex' are courtesy of [46] and [47], respectively. All other meshes are Cartesian meshes.…”

“…All other meshes are Cartesian meshes. 'Arched Bridge', 'Parts' and 'Rod' are courtesy of [48], [46] and [47], respectively. All simulated stress fields are made publicly available.…”