Structured Volume Decomposition via Generalized Sweeping

Representing digital objects with structured meshes that embed a coarse block decomposition is a relevant problem in applications like computer animation, physically-based simulation and Computer Aided Design (CAD). One of the key ingredients to produce coarse block structures is to achieve a good alignment between the mesh singularities (i.e., the corners of each block). In this paper we improve on the polycube-based meshing pipeline to produce both surface and volumetric coarse block-structured meshes of general shapes. To this aim we add a new step in the pipeline. Our goal is to optimize the positions of the polycube corners to produce as coarse as possible base complexes. We rely on re-mapping the positions of the corners on an integer grid and then using integer numerical programming to reach the optimal. To the best of our knowledge this is the first attempt to solve the singularity misalignment problem directly in polycube space. Previous methods for polycube generation did not specifically address this issue. Our corner optimization strategy is efficient and requires a negligible extra running time for the meshing pipeline. In the paper we show that our optimized polycubes produce coarser block structured surface and volumetric meshes if compared with previous approaches. They also induce higher quality hexahedral meshes and are better suited for spline fitting because they reduce the number of splines necessary to cover the domain, thus improving both the efficiency and the overall level of smoothness throughout the volume

Section: Related Workmentioning

confidence: 99%

Polycube Simplification for Coarse Layouts of Surfaces and Volumes

Cherchi

Livesu

Scateni

2016

“…Paving and Sweeping. The first generation of hex‐meshing algorithms was based on paving (i.e., inserting layers of cubes on a quad mesh boundary) and sweeping (i.e., extruding a quad mesh or a skeleton) [SJ08, GMD*16, LMPS16]. While ideal to produce high‐quality elements in the vicinity of the boundary, the quality of the generated elements is poor in the interior where the multiple advancing fronts meet.…”

Section: Related Workmentioning

confidence: 99%

Feature Preserving Octree‐Based Hexahedral Meshing

Gao

Shen

Panozzo

2019

Self Cite

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.

“…These singularities help define the base complex of the hex‐mesh. A large number of singularities may result in a base complex with many hexahedral components, posing challenges for the fitting of basic functions with higher order smoothness for the subsequent simulations [GDC15, GMD*16]. The recently proposed adaptive hex‐meshing techniques [ZZ07, SZ16] based on a similar framework to the octree‐based approach still do not address the issue of introducing an excessive number of singularities.…”

Section: Related Workmentioning

confidence: 99%

“…[JHW*14] also aims to derive a restricted cross field from some initial cross field, which is then used to generate hex‐meshes by solving a mixed‐integer problem. Despite generating hex‐meshes with superior quality, frame‐field‐based methods are typically less robust, compared to the polycubes approach, and can easily lead to degeneracy in the parameterization [LLX*12, GMD*16].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Hexahedral Meshing With Varying Element Sizes

Gao

Deng

et al. 2017

Self Cite

Hexahedral (or Hex‐) meshes are preferred in a number of scientific and engineering simulations and analyses due to their desired numerical properties. Recent state‐of‐the‐art techniques can generate high‐quality hex‐meshes. However, they typically produce hex‐meshes with uniform element sizes and thus may fail to preserve small‐scale features on the boundary surface. In this work, we present a new framework that enables users to generate hex‐meshes with varying element sizes so that small features will be filled with smaller and denser elements, while the transition from smaller elements to larger ones is smooth, compared to the octree‐based approach. This is achieved by first detecting regions of interest (ROIs) of small‐scale features. These ROIs are then magnified using the as‐rigid‐as‐possible deformation with either an automatically determined or a user‐specified scale factor. A hex‐mesh is then generated from the deformed mesh using existing approaches that produce hex‐meshes with uniform‐sized elements. This initial hex‐mesh is then mapped back to the original volume before magnification to adjust the element sizes in those ROIs. We have applied this framework to a variety of man‐made and natural models to demonstrate its effectiveness.