An approach to automated decomposition of volumetric mesh

Mesh decomposition is critical for analyzing, understanding, editing and reusing of mesh models. Although there are many methods for mesh decomposition, most utilize only triangular meshes. In this paper, we present an automated method for decomposing a volumetric mesh into semantic components. Our method consists of three parts. First, the outer surface mesh of the volumetric mesh is decomposed into semantic features by applying existing surface mesh segmentation and feature recognition techniques. Then, for each recognized feature, its outer boundary lines are identified, and the corresponding splitter element groups are setup accordingly. The inner volumetric elements of the feature are then obtained based on the established splitter element groups. Finally, each splitter element group is decomposed into two parts using the graph cut algorithm; each group completely belongs to one feature adjacent to the splitter element group. In our graph cut algorithm, the weights of the edges in the dual graph are calculated based on the electric field, which is generated using the vertices of the boundary lines of the features. Experiments on both tetrahedral and hexahedral meshes demonstrate the effectiveness of our method.     

子分元素法:一种体网格压缩算法

提出了一个包含六面体,四面体,金字塔以及三棱柱单元的混合体网格的压缩与解压算法。首先对非四面体单元按照最小节点标号策略进行子分,然后利用修改的增长缝合算法压缩子分后的四面体网格,解压阶段再通过面删除操作来恢复原始网格。压缩后每个四面体约需10bits的存储,初步试验表明,对于通常的六面体网格,能将数据模型压缩至原先的1／4。     

Forming and resolving wedges in the spatial twist continuum

The spatial twist continuum (STC) is a powerful extension of the dual of a hexahedral mesh Murdochet al.,Int. J. Numer. Math. Engng (submitted). The STC captures the global connectivity constraints inherent in hexahedral meshing. Whisker wwaving is an advancing-front type of algorithm based on the STC[Tautges et al., Int. J. Numer. Math. Engng (submitted]. During the whisker weaving algorithm, certain types of degenerate elements calledwedges [Biacker; Myers (1993)Engng with Computers 9, 83–93 arise. This paper describedwedges and how they are formed, and presentscollapsing anddriving, two strategies for removing these degeneracies.     

SUSAN structure preserving filtering for mesh denoising

Motivated by the impressive effect of the SUSAN operator for low level image processing and its usage simplicity, we extend it to denoise the 3D mesh. We use the angle between the normals on the surface to determine the SUSAN area; each point has associated itself with the SUSAN area that is has a similar continuity feature to the point. The SUSAN area avoids the feature to be taken as noise effectively, so the SUSAN operator gives the maximal number of suitable neighbors with which to take an average, whilst no neighbors from unrelated regions are involved. Thus, the entire structure can be preserved. We also extend the SUSAN operator to two-ring neighbors by a squared umbrella-operator to improve the surface smoothness with little loss of detailed features. Details of the SUSAN structure preserving noise reduction algorithm are discussed along with the test results in this paper.     

HEXHOOP: Modular Templates for Converting a Hex-Dominant Mesh to an ALL-Hex Mesh

This paper presents a new mesh conversion template called HEXHOOP, which fully automates a con-version from a hex-dominant mesh to an all-hex mesh. A HEXHOOP template subdivides a hex/prism/pyramid element into a set of smaller hex elements while main-taining the topological conformity with neighboring elements. A HEXHOOP template is constructed by assembling sub-templates, cores and caps. A dicing template for a hex and a prism is constructed by choosing the appropriate combination of a core and caps. A template that dices a pyramid without losing conformity to the adjacent element is derived from a HEXHOOP template. Some experimental results show that the HEXHOOP templates successfully convert a hex-dominant mesh into an all-hex mesh. ID="A1" Correspondence and offprint requests to: K. Shimada, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213–3890, USA. E-mail: shimada@cmu.edu     

A comparison of two optimization methods for mesh quality improvement

We compare inexact Newton and block coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.

Automated Conformal Hexahedral Meshing Constraints, Challenges and Opportunities

Automated hexahedral element meshing has been the ‘Holy Grail’ of mesh generation research for years. The rigid connectivity and shape constraints of these meshes provide the challenge. The ever-present economic pressure for automating meshing of complex geometries, difficult transitions and large mesh sizes establishes the opportunity. This paper will systematically review the requirements of the hexahedral meshing challenge, the various approaches to the solution of the problem (along with their respective attributes), and some musings about future research opportunities.     

基于拉普拉斯算子的三角网格模型的平滑与压缩算法

三角网格模型被广泛应用于各个领域并迅速发展,为了既保留网格模型的局部几何特征,又在平滑去噪的同时能够较好地保持边缘、纹理等细节信息,提出一种基于拉普拉斯算子的偏微分方程平滑方法,可以得到较好的去噪效果;为了更加方便三维数据的传输与操作,采用了一种在拉普拉斯算子的基础上,对三角网格模型进行特征分解进而进行光谱压缩的方法,可以实现对模型的压缩.     

The geometric element transformation method for mixed mesh smoothing

The geometric element transformation method (GETMe) is a geometry-based smoothing method for mixed and non-mixed meshes. It is based on a simple geometric transformation applicable to elements bounded by polygons with an arbitrary number of nodes. The transformation, if applied iteratively, leads to a regularization of the polygons. Global mesh smoothing is accomplished by averaging the new node positions obtained by local element transformations. Thereby, the choice of transformation parameters as well as averaging weights can be based on the element quality which leads to high quality results. In this paper, a concept of an enhanced transformation approach is presented and a proof for the regularizing effect of the transformation based on eigenpolygons is given. Numerical examples confirm that the GETMe approach leads to superior mesh quality if compared to other geometry-based methods. In terms of quality it can even compete with optimization-based techniques, despite being conceptually significantly simpler.     

Using a computational domain and a three-stage node location procedure for multi-sweeping algorithms

The multi-sweeping method is one of the most used algorithms to generate hexahedral meshes for extrusion volumes. In this method the geometry is decomposed in sub-volumes by means of projecting nodes along the sweep direction and imprinting faces. However, the quality of the final mesh is determined by the location of inner nodes created during the decomposition process and by the robustness of the imprinting process.In this work we present two original contributions to increase the quality of the decomposition process. On the one hand, to improve the robustness of the imprints we introduce the new concept of computational domain for extrusion geometries. Since the computational domain is a planar representation of the sweep levels, we improve several geometric operations involved in the imprinting process. On the other hand, we propose a three-stage procedure to improve the location of the inner nodes created during the decomposition process. First, inner nodes are projected towards source surfaces. Second, the nodes are projected back towards target surfaces. Third, the final position of inner nodes is computed as a weighted average of the projections from source and target surfaces.     

A local cell quality metric and variational grid smoothing algorithm

A local cell quality metric is introduced and used to construct a variational functional for a grid smoothing algorithm. A maximum principle is proved and the properties of the local quality measure, which combines element shape and size control metrics, are investigated. Level set contours are displayed to indicate the effect of cell distortion. The approach is demonstrated for meshes of triangles and quadrilaterals in 2D and a test case with hexahedral cells in 3D. Issues such as the use of a penalty for folded meshes and the effect of valence change in the mesh patches are considered.     

A Case Study in Hexahedral Mesh Generation: Simulation of the Human Mandible

We provide a case study for the generation of pure hexahedral meshes for the numerical simulation of physiological stress scenarios of the human mandible. Du to its complex and very detailed free-form geometry, the mandible model is very demanding. This test case is used as a running example to demonstrate the applicability of a combinatorial approach for the generation of hexahedral meshes by means of successive dual cycle eliminations, which has been proposed by the second author in previous work. We report on the progress and recent advances of the cycle elimination scheme. The given input data, a surface triangulation obtained from computed tomography data, requires a substantial mesh reduction and a suitable conversion into a quadrilateral surface mesh as a first step, for which we use mesh clustering and b-matching techniques. Several strategies for improved cycle elimination orders are proposed. They lead to a significant reduction in the mesh size and a better structural quality. Based on the resulting combinatorial meshes, gradient-based optimized smoothing with the condition number of the Jacobian matrix as objective together with mesh untangling techniques yielded embeddings of a satisfactory quality. To test our hexahedral meshes for the mandible model within an FEM simulation we used the scenario of a bite on a ‘hard nut.’ Our simulation results are in good agreement with observations from biomechanical experiments.     

Hexahedral mesh generation constraints

For finite element analyses within highly elastic and plastic structural domains, hexahedral meshes have historically offered some benefits over tetrahedral finite element meshes in terms of reduced error, smaller element counts, and improved reliability. However, hexahedral finite element mesh generation continues to be difficult to perform and automate, with hexahedral mesh generation taking several orders of magnitude longer than current tetrahedral mesh generators to complete. Thus, developing a better understanding of the underlying constraints that make hexahedral meshing difficult could result in dramatic reductions in the amount of time necessary to prepare a hexahedral finite element model for analysis. In this paper, we present a survey of constraints associated with hexahedral meshes (i.e., the conditions that must be satisfied to produce a hexahedral mesh). In presenting our formulation of these constraints, we will utilize the dual of a hexahedral mesh. We also discuss how incorporation of these constraints into existing hexahedral mesh generation algorithms could be utilized to extend the class of geometries to which these algorithms apply. We also describe a list of open problems in hexahedral mesh generation and give some context for future efforts in addressing these problems.     

A grid-based algorithm for the generation of hexahedral element meshes

An algorithm for the generation of hexahedralelement meshes is presented. The algorithm works in two steps: first the interior of the volume is filled with a regular grid; then the boundary region is meshed by using basically twodimensional operations.The algorithm was designed for use in the fem-simulation of metal forming processes where a remeshing must be done very often. In principle, it can be used for meshing any geometry with hexahedral elements and examples of meshes for geometries arising from various applications are given. The algorithm is checked against the criteria proposed by Sabin [1] (Advances in Engineering Software, 13, 220–225).     

Hexahedral and Tetrahedral Mesh Untangling

We investigate a well-motivated mesh untangling objective function whose optimization automatically produces non-inverted elements when possible. Examples show the procedure is highly effective on tetrahedral meshes and on many hexahedral meshes constructed via mapping or sweeping algorithms.     

基于切平面中值坐标的Laplacian网格变形算法

网格模型变形往往需要保持局部几何细节,Laplacian网格变形算法能够较好地保持局部几何细节特征,但细节特征描述子-Laplacian坐标的计算欠缺精确性.从平面多边形中值坐标的角度出发,对Laplacian坐标进行重新定义,将顶点的一阶邻域投影到顶点处切平面上,根据顶点相对投影点的中值坐标构建的Laplacian坐标能够精确地描述模型的局部几何细节特征,实验验证能够获得较好的编辑效果.     

High-order curvilinear meshing using a thermo-elastic analogy

With high-order methods becoming increasingly popular in both academia and industry, generating curvilinear meshes that align with the boundaries of complex geometries continues to present a significant challenge. Whereas traditional low-order methods use planar-faced elements, high-order methods introduce curvature into elements that may, if added naively, cause the element to self-intersect. Over the last few years, several curvilinear mesh generation techniques have been designed to tackle this issue, utilizing mesh deformation to move the interior nodes of the mesh in order to accommodate curvature at the boundary. Many of these are based on elastic models, where the mesh is treated as a solid body and deformed according to a linear or non-linear stress tensor. However, such methods typically have no explicit control over the validity of the elements in the resulting mesh. In this article, we present an extension of this elastic formulation, whereby a thermal stress term is introduced to ‘heat’ or ‘cool’ elements as they deform. We outline a proof-of-concept implementation and show that the adoption of a thermo-elastic analogy leads to an additional degree of robustness, by considering examples in both two and three dimensions.     

任意拓扑结构网格模型自适应调整和光顺算法

在改进拉普拉斯算子的同时,吸取平均曲率法的优点,提出一种任意网格模型自适应调整和光顺算法．该算法通过沿法矢方向和在切平面上同时对网格顶点进行调整,保证了调整后模型不仅光顺,而且网格形状均匀;该算法还可以根据不同的精度自动地对网格调整进行控制,有效地保留了原始模型中的特征信息．应用实例表明,该算法可以保证在满足精度要求的条件下,得到更合理的三角网格模型．