Adaptive tetrahedral remeshing for modified solid models

During the engineering design process, a designed engineering component is usually repeatedly modified and analyzed to reach final design objectives, and completely mesh regeneration for each design change is very time consuming. An efficient remeshing approach for modified solid models using existing prior existing meshes is proposed in this paper to resolve this issue. It is mainly achieved via three main steps: different face (between the input model and its modification) identification, local destruction zone generation, and local mesh regeneration. In this approach, by carefully selecting a destruction zone to be removed from the original mesh model, a final geometric adaptive mesh model of the modified model is generated, which is very important for downstream analysis accuracy control. Additionally, the complex boundary of the variation region that needs to be remeshed is set up by merging the boundaries of modified region and the destruction zone without using complex intersection operations, which ensure the approach’s robustness. Experimental results on practical engineering parts are also shown to demonstrate the method’s performance.     

Image Processing to Automate Mesh Generation

Finite element modeling is now a standard approach used in the industry to minimize costly trials and help reduce the overall lead time in product and process design. However, building surface/solid models defining the product shape and generating finite element meshes for analyses still require a significant amount of the engineers’ time. In this paper, we present a new method for automatically generating a finite element mesh directly from bitmap images obtained from an artist’s concept of a label for an embossed aluminum beverage can, and demonstrate its application towards the building of tooling mesh models used in the modeling of the embossing process. This approach completely eliminates the need for creating a surface/solid model, thus resulting in a dramatic reduction in the time required for process design.     

Embedded Implicit Stand-Ins for Animated Meshes: A Case of Hybrid Modelling

In this paper, we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid-modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. We model the interaction between an animated mesh object and a viscoelastic substance, which is normally represented in an implicit form. Our approach is aimed at achieving verisimilitude rather than physically based simulation. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented.     

车身冲压模型腔表面四边形网格的局部粗化

给定一车身冲压模型腔表面上结构化的四边形网格，通过单元合并对网格进行自动的粗化，其目的在于简化冲压仿真模型，提高仿真计算速度，首先，根据单元节点曲率半径的分布，搜寻出满足单元合并条件的初始四边形区域，接头，判断初始合交区域的边界过渡条件，最后，进行单合并，冲压成型仿真应用实例证明，文中算法既提高了仿真速度，又保持了仿真精度，该算法可以推广到任意曲面结构化四边形网格的局部粗化问题。     

Tetrahedral finite element mesh generation from NURBS solid models

In this paper, the development and the implementation of a tetrahedral meshing algorithm for generation of finite element meshes from NURBS solid models is presented. The meshing algorithm is based on a Delaunay technique, and makes use of some spatial data structures. The algorithm is capable of generating both uniform and varying size four-node and ten-node tetrahedral meshes. The algorithm has been implemented in a building block approach as part of a software library. It has been used as a practical tool in engineering design processes. Several representative test cases illustrate the effectiveness of the automatic solid mesh generator.     

Automatic hexahedral mesh generation for multi-domain composite models using a hybrid projective grid-based method

This paper presents an algorithm to generate an all-hexahedral mesh of a multi-domain solid model using a hybrid grid-based approach. This is based on a projective concept during the boundary adaptation of the initial mesh. In general, the algorithm involves the generation of a grid structure, which is superimposed on the solid model. This grid structure forms an initial mesh consisting of hexahedral elements, which intersect fully or partially with the solid model. This initial mesh is then shrunk in an outside-in manner to the faces of the model through a node projection process using the closest position approach. To match the resulting mesh to the edges of the model, a minimal deformation angle method is used. Finally, to match the vertices with the nodes on the mesh, a minimal warp angle method is employed. To create the mesh of a multi-domain solid model, an outside-in and inside-in hybrid of the grid-based method is used. This hybrid method ensures that the meshes of the different domains are conforming at their common boundary. This paper also describes two methods for resolving cases of degenerate elements: a splitting technique and a wedge insertion technique.     

Computing on rays: A parallel approach for surface mesh modeling from multi-material volumetric data

Ray representation (Ray-rep) of a solid has been studied and used in the solid modeling community for many years because of its compactness and simplicity. This paper presents a parallel approach for mesh surface modeling from multi-material volume data using an extended Ray-rep as an intermediate, where every homogeneous region is enclosed by a set of two-manifold surface meshes on the resultant model. The approach consists of three major algorithms: firstly, an algorithm is developed to convert the given multi-material volumetric data into a Ray-rep for heterogeneous solid; secondly, filtering algorithm is exploited to process the rays of heterogeneous solid in parallel; and lastly, the adaptive mesh surfaces are generated from the Ray-rep through a dual-contouring like algorithm. Here the intermediate surfaces between two constituent materials can be directly extracted without building the volumetric mesh, and the manifold topology is preserved on each surface patch. Furthermore, general offset surface can be easily computed in this paradigm by designing a special parallel operator for the rays.     

A control approach for pore size distribution in the bone scaffold based on the hexahedral mesh refinement

Tissue engineering is the application of that knowledge to the building or repairing of tissues. Generally, engineered tissue is a combination of living cells and a support structure called scaffolds. Modeling, design and fabrication of tissue scaffold with intricate architecture, porosity and pore size for desired tissue properties presents a challenge in tissue engineering. In this paper, a control approach for pore size distribution in the bone scaffold based on the hexahedral mesh refinement is presented. Firstly, the bone scaffold modeling approach based on the shape function in the finite element method is provided. The resulting various macroporous morphologies can be obtained. Then conformal refinement algorithm for all-hexahedral element mesh is illustrated. Finally, a modeling approach for constructing tissue engineering (TE) bone scaffold with defined pore size distribution is presented. Before the conformal refinement of all-hexahedral element mesh, a 3D mesh with various hexahedral elements must be provided. If all the pores in the bone scaffold need to be reduced, that means that the whole hexahedral mesh needs to be refined. Then the solid entity can be re-divided with altered subdivision parameters. If the pores in the local regions of bone need to be reduced, that means that 3D hexahedral mesh in the local regions needs to be refined. Based on SEM images, the pore size distribution in the normal bone can be obtained. Then, according to the conformal refinement of all-hexahedral element meshes, defined hexahedral size distribution can be gained, which leads to generate defined pore size distribution in the bone scaffold, for the pore morphology and size are controlled by various subdivided hexahedral elements. Compared to other methods such as varying processing parameters in supercritical fluid processing and multi-interior architecture design, the method proposed in this paper enjoys easy-controllability and higher accuracy.     

复杂开曲面的鲁棒布尔运算

在计算机辅助几何设计中,布尔运算是一种构造实体的常用方法。自从19 世纪 80 年代布尔运算被提出后,该方向的研究工作大多是在效率与鲁棒性间做权衡,为了保证输入 网格表示某个实体的边界,大部分算法严格要求其没有洞和边界边。故此提出一种与上不同的 高效的、鲁棒的适用广的布尔运算算法,其能在非实体网格上被执行。首先,将输入网格合并, 然后在解决合并出现的自交问题后,将网格沿着非流形边分割成许多不同的流形块,并且检测 出流形块所围成的胞体;然后通过添加虚拟流形块的方法计算胞体的环绕数,并标记胞体关于 输入网格的属性,从而得到正确的布尔运算结果。     

Template-based quadrilateral meshing

Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthogonality, alignment and adaptivity; however, they cannot make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features.     

Adaptive generation of hexahedral element mesh using an improved grid-based method

An improved grid-based algorithm for the adaptive generation of hexahedral finite element mesh is presented in this paper. It is named as the inside-out grid-based method and involves the following four steps. The first step is the generation of an initial grid structure which envelopes the analyzed solid model completely. And the elements size and density maps are constructed based on the surface curvature and local thickness of the solid model. Secondly, the core mesh is generated through removing all the undesired elements using even and odd parity rules. The third step is to magnify the core mesh in an inside-out manner through a surface node projection process using the closest position approach. To match the mesh to the characteristic boundary of the solid model, a minimal Scaled Jacobian criterion is employed. Finally, in order to handle the degenerated elements and improve the quality of the resulting mesh, two comprehensive techniques are employed: the insertion technique and collapsing technique. The present method was applied in the mesh construction of different engineering problems. Scaled Jacobian and Skew metrics are used to evaluate the hexahedral element mesh quality. The application results show that all-hexahedral element meshes which are well-shaped and capture all the geometric features of the original solid models can be generated using the inside-out grid-based method presented in this paper.     

TUM.GeoFrame: automated high-order hexahedral mesh generation for shell-like structures

This paper presents a fully automated high-order hexahedral mesh generation algorithm for shell-like structures based on enhanced sweeping methods. Traditional sweeping techniques create all-hexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming high-order all-hexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skew-angled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a so-called interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.     

Anisotropic quadrilateral mesh generation: An indirect approach

In this paper a new indirect approach is presented for anisotropic quadrilateral mesh generation based on discrete surfaces. The ability to generate grids automatically had a pervasive influence on many application areas in particularly in the field of Computational Fluid Dynamics. In spite of considerable advances in automatic grid generation there is still potential for better performance and higher element quality. The aim is to generate meshes with less elements which fit some anisotropy criterion to satisfy numerical accuracy while reducing processing times remarkably. The generation of high quality volume meshes using an advancing front algorithm relies heavily on a well designed surface mesh. For this reason this paper presents a new technique for the generation of high quality surface meshes containing a significantly reduced number of elements. This is achieved by creating quadrilateral meshes that include anisotropic elements along a source of anisotropy.     

Spectral mesh deformation

In this paper, we present a novel spectral method for mesh deformation based on manifold harmonics transform. The eigenfunctions of the Laplace–Beltrami operator give orthogonal bases for parameterizing the space of functions defined on the surfaces. The geometry and motion of the original irregular meshes can be compactly encoded using the low-frequency spectrum of the manifold harmonics. Using the spectral method, the size of the linear deformation system can be significantly reduced to achieve interactive computational speed for manipulating large triangle meshes. Our experimental results demonstrate that only a small spectrum is needed to achieve undistinguishable deformations for large triangle meshes. The spectral mesh deformation approach shows great performance improvement on computational speed over its spatial counterparts.     

Generation of Tetrahedral Meshes with Multiple Elements through Thin Sections

Finite element simulations in domains with strong gradients across thin sections typically require meshes with multiple elements through these sections to accurately capture the solution. Most of the published techniques for isotropic mesh generation are not suited for the creation of such meshes in general, arbitrarily complex, non-manifold domains. In this paper, an automatic method is described for identification of thin sections of a domain and anisotropic refinement of an initial mesh to introduce a user-requested number of elements through the thin sections. The method uses local mesh modification operations to effect the refinement and subsequent realignment of edges along the thickness direction and perpendicular to it. Results are presented for a number of general models to illustrate the capability of the mesh generator.     

Hexahedral Mesh Generation by Successive Dual Cycle Elimination

We propose a new method for constructing all-hexahedral finite element meshes. The core of our method is to build up a compatible combinatorial cell complex of hexahedra for a solid body which is topologically a ball, and for which a quadrilateral surface mesh of a certain structure is prescribed. The step-wise creation of the hex complex is guided by the cycle structure of the combinatorial dual of the surface mesh. Our method transforms the graph of the surface mesh iteratively by changing the dual cycle structure until we get the surface mesh of a single hexahedron. Starting with a single hexahedron and reversing the order of the graph transformations, each transformation step can be interpreted as adding one or more hexahedra to the so far created hex complex. Given an arbitrary solid body, we first decompose it into simpler subdomains equivalent to topological balls by adding virtual 2-manifolds. Secondly, we determine a compatible quadrilateral surface mesh for all subdomains created. Then, in the main part we can use the core routine to build up a hex complex for each subdomain independently. The embedding and smoothing of the combinatorial mesh(es) finishes the mesh generation process. First results obtained for complex geometries are encouraging.     

Automatic p-version mesh generation for curved domains

To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains, these meshes are characterized by having large curved elements over smooth portions of the domain and geometrically graded curved elements to isolate the edge and vertex singularities that are of interest. This paper presents a procedure under development for the automatic generation of such meshes for general three-dimensional domains defined in solid modeling systems. Two key steps in the procedure are the determination of the singular model edges and vertices, and the creation of geometrically graded elements around those entities. The other key step is the use of general curved element mesh modification procedures to correct any invalid elements created by the curving of mesh entities on the model boundary, which is required to ensure a properly geometric approximation of the domain. Example meshes are included to demonstrate the features of the procedure.

基于Hermite插值的网格拼接和融合-CIDE2013

网格模型的拼接和融合是3维形状编辑和造型中的一个重要方面。基于Hermite插值技术,提出了一种适用于具有一般边界点空间分布的三角网格模型之间无缝光滑拼接和融合方法。首先查找网格模型待拼接区域的边缘点集,并利用二次B样条曲线插值边缘点集分别得到边缘曲线;然后对边缘曲线进行Hermite插值得到拼接区域连续曲面;最后对拼接曲面分别进行三角网格化和Laplacian光顺平滑处理以实现网格模型的光滑拼接和融合。由于利用B样条曲线插值待拼接模型边界,本文方法适用于具有各种不同边界情形的网格模型拼接和融合,它不仅仅可以处理平面边界曲线情形也可以处理空间边界曲线情形。结合Hermite曲面插值拼接过渡区域,使得产生的拼接网格能光滑地衔接待拼接模型。实验结果表明,本文方法能够有效地实现三角网格模型的光滑拼接、模型修复和模型融合。     

基于Hermite插值的网格拼接和融合

网格模型的拼接和融合是3维形状编辑和造型中的一个重要方面。基于Hermite插值技术,提出一种适用于具有一般边界点空间分布的三角网格模型之间无缝光滑拼接和融合方法。首先查找网格模型待拼接区域的边缘点集,并利用二次B样条曲线插值边缘点集分别得到边缘曲线;然后对边缘曲线进行Hermite插值得到拼接区域连续曲面;最后对拼接曲面分别进行三角网格化和Laplacian光顺平滑处理以实现网格模型的光滑拼接和融合。由于利用B样条曲线插值待拼接模型边界,本文方法适用于具有各种不同边界情形的网格模型拼接和融合,它不仅仅可以处理平面边界曲线情形也可以处理空间边界曲线情形。结合Hermite曲面插值拼接过渡区域,使得产生的拼接网格能光滑地衔接待拼接模型。实验结果表明,本文方法能够有效地实现三角网格模型的光滑拼接、模型修复和模型融合。