Hexagon-based all-quadrilateral mesh generation with guaranteed angle bounds

In this paper, we present a novel hexagon-based mesh generation method which creates all-quadrilateral (all-quad) meshes with guaranteed angle bounds and feature preservation for arbitrary planar domains. Given any planar curves, an adaptive hexagon-tree structure is constructed by using the curvature of the boundaries and narrow regions. Then a buffer zone and a hexagonal core mesh are created by removing elements outside or around the boundary. To guarantee the mesh quality, boundary edges of the core mesh are adjusted to improve their formed angles facing the boundary, and two layers of quad elements are inserted in the buffer zone. For any curve with sharp features, a corresponding smooth curve is firstly constructed and meshed, and then another layer of elements is inserted to match the smooth curve with the original one. It is proved that for any planar smooth curve all the element angles are within [60° ? ε, 120° + ε] (ε ? 5°). We also prove that the scaled Jacobians defined by two edge vectors are in the range of [sin (60° ? ε),  sin 90°], or [0.82, 1.0]. The same angle range can be guaranteed for curves with sharp features, with the exception of small angles in the input curve. Furthermore, an approach is introduced to match the generated interior and exterior meshes with a relaxed angle range, [30°, 150°]. We have applied our algorithm to a set of complicated geometries, including the China map, the Lake Superior map, and a three-component air foil with sharp features. In addition, all the elements in the final mesh are grouped into five types, and most elements only need a few flops to construct the stiffness matrix for finite element analysis. This will significantly reduce the computational time and the required memory during the stiffness matrix construction.     

Guaranteed-quality anisotropic mesh generation for domains with curved boundaries

Anisotropic mesh generation is important for interpolation and numerical modeling. Recently, Labelle and Shewchuk proposed a two-dimensional guaranteed-quality anisotropic mesh generation algorithm called a Voronoi refinement algorithm. This algorithm treats only domains with straight lines as inputs. In many applications, however, input domains have many curves and the exact representation of curves is required for efficient numerical modeling. In this paper, we extend the Voronoi refinement algorithm and propose it as a guaranteed-quality anisotropic mesh generation algorithm for domains with curved boundaries. Some experimental results are also shown.     

医学体数据中基于局部特征尺寸的Delaunay四面体化算法*

为了从医学体数据构建面向虚拟手术仿真系统的器官实体模型,提出一种基于局部特征尺寸的Delaunay四面体化算法。首先采用Marching Cubes算法和外存模型简化技术从体数据中得到器官等值面简化模型,提出重心射线法去除内部冗余网格,获得器官多面体表面;然后基于局部特征尺寸构建表面顶点保护球,结合Delaunay细分算法生成边界一致的初始四面体网格;最后提出基于随机扰动的空间分解法快速生成内部节点,并逐点插入到四面体网格中优化单元质量。该算法克服了Delaunay细分算法无法处理锐角输入的缺点,并从理论     

Volumetric subspace mesh deformation with structure preservation

Existing deformation techniques are oblivious to salient structures that often capture the essence of 3D meshes. Combining with gradient domain technique, we propose an alternative approach to preserve these structures in the volumetric subspace. Through a simple sketching interface, the structures of the input mesh are specified by the user. During deformations, these key structures are constrained to deform rigidly to maintain their original shapes, hence avoiding serious visual artifacts. However, this process leads to a nonlinear optimization problem. To guarantee fast convergence as well as numerical stability, we project the deformation energy onto a volumetric subspace which envelops the input mesh. Then the energy optimization is performed in this subspace to greatly facilitate the editing of large meshes. Massive experimental data demonstrate the effectiveness and efficiency of our algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

保持属性特征的模型简化算法*

为较好保持模型的拓扑结构和属性特征,采用基于半边折叠简化思想对模型进行了带属性简化算法的研究。算法考虑了几何误差度量算子的三个因子：折叠边的欧氏距离、折叠边二面角和顶点到星型邻域平面的距离;引入模型属性特征权重值,将几何误差和属性误差加权作为总体误差进行简化,并对简化质量进行了合法性检查。实验证明,算法在保持模型几何和属性特征方面有效。     

保特征的联合滤波网格去噪算法

目的 在去噪的过程中保持网格模型的特征结构是网格去噪领域研究的热点问题。为了能够在去噪中保持模型特征,本文提出一种基于变分形状近似（VSA）分割算法的保特征网格去噪算法。方法 引入变分形状近似分割算法分析并提取噪声网格模型的几何特征,分3步进行去噪。第1步使用变分形状近似算法对网格进行分割,对模型进行分块降噪预处理。第2步通过分析变分形状近似算法提取分割边界中的特征信息,将网格划分为特征区域与非特征区域。对两个区域用不同的滤波器联合滤波面法向量。第3步根据滤波后的面法向量,使用非迭代的网格顶点更新方法更新顶点位置。结果 相较于现有全局去噪方法,本文方法可以很好地保持网格模型的特征,引入的降噪预处理对于非均匀网格的拓扑结构保持有着很好的效果。通过对含有不同程度高斯噪声的网格模型进行实验表明,本文算法无论在直观上还是定量分析的结果都相较于对比的方法有着更好的去噪效果,实验中与对比算法相比去噪效果提升15%。结论 与现有的网格去噪算法对比,实验结果表明本文算法在中等高斯噪声下更加鲁棒,对常见模型有着比较好的去噪效果,能更好地处理不均匀采样的网格模型,恢复模型原有的特征信息和拓扑结构。     

CAD mesh model simplification with assembly features preservation

This paper aims to investigate a CAD mesh model simplification method with assembly features preservation, in order to satisfy the requirement of assembly field for the information of 3D model. The proposed method simplifies a CAD mesh model as follows. Firstly, the notion of ＂conjugation＂ is incorporated into the definition of assembly features, with the purpose of benefitting the downstream applications such as assembly features recognition and preservation. Subsequently, the attributed adjacency graphs （AAGs） of the region- level-represented parts are established. The assembly features are automatically recognized by searching for conjugated subgraphs of every two AAGs based on subgraph isomorphism algorithm. In order to improve the efficiency of assembly features recognition, the characteristics of conjugated subgraphs are adopted to initialize the mapping matrix, and the ＂verifying while matching strategy＂ is used to verify the validity of every two newly founded vertices which are correspondingly matched. Then, simplified CAD mesh model with assembly features preserved is constructed after suppressing the common form features. The method is applied successfully to simplify the CAD mesh model with assembly features well preserved. Moreover, the tradeoff between the cost of time for conjugated subgraphs matching and the complexity of the to-be-matched parts is proven to be almost linear.     

Polygon crawling: feature edge extraction from a general polygonal surface for mesh generation

This article describes a method for extracting feature edges of a polygonal surface for mesh generation. This method can extract feature edges from a polygonal surface typically created by a CAD facet generator in which typical feature edge extraction methods fail due to severe nonuniformity and anisotropy. The method is based on the technique called “polygon crawling,” which samples a sequence of points on the polygonal surface by moving a point along the polygonal surface. Extracting appropriate feature edges is important for creating a coarse mesh without yielding self-intersections. Extensive tests have been performed with various CAD-generated facet models, and this technique has shown good performance in extracting feature edges.     

Surface feature based mesh segmentation

Mesh segmentation has a variety of applications in product design, reverse engineering, and rapid prototyping fields. This paper presents a novel algorithm of mesh segmentation from original scanning data points, which essentially consists of three steps. Normal based initial decomposing is first performed to recognize plane features. Then we implement further segmentation based on curvature criteria and Gauss mapping, followed by the detection of quadric surface features. The segmentation refinement is finally achieved using B-spline surface fitting technology. The experimental results on many 3D models have demonstrated the effectiveness and robustness of the proposed segmentation method.     

Finite element mesh generation

The capabilities of a geometric modeller are extended towards finite element analysis by a mesh generator which extracts all its geometric and topological information from the model. A coarse mesh is created and subsequently refined to a suitable finite element mesh, which accomodates material properties, loadcase and analysis requirements. The mesh may be optimized by adaptive refinement, ie according to estimates of the discretization errors.A survey of research and development in geometric modelling and finite element analysis is presented, then an implementation of a mesh generator for 3D curvilinear and solid objects is described in detail.     

Parallel adaptive mesh generation

Unstructured meshes have proved to be a powerful tool for adaptive remeshing of finite element idealizations. This paper presents a transputer-based parallel algorithm for two dimensional unstructured mesh generation. A conventional mesh generation algorithm for unstructured meshes is reviewed by the authors, and some program modules of sequential C source code are given. The concept of adaptivity in the finite element method is discussed to establish the connection between unstructured mesh generation and adaptive remeshing.After these primary concepts of unstructured mesh generation and adaptivity have been presented, the scope of the paper is widened to include parallel processing for un-structured mesh generation. The hardware and software used is described and the parallel algorithms are discussed. The Parallel C environment for processor farming is described with reference to the mesh generation problem. The existence of inherent parallelism within the sequential algorithm is identified and a parallel scheme for unstructured mesh generation is formulated. The key parts of the source code for the parallel mesh generation algorithm are given and discussed. Numerical examples giving run times and the consequent “speed-ups” for the parallel code when executed on various numbers of transputers are given. Comparisons between sequential and parallel codes are also given. The “speed-ups” achieved when compared with the sequential code are significant. The “speed-ups” achieved when networking further transputers is not always sustained. It is demonstrated that the consequent “speed-up” depends on parameters relating to the size of the problem.     

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.     

方向感知的网格模型特征识别

针对网格模型平滑区域提取特征困难,以及现有特征识别方法无法检测仅沿某一特定方向分布的特征点的问题,提出一种方向感知的网格模型特征识别方法。首先,分别从x、y、z三个方向探测网格顶点邻接面法向量沿不同方向变化的情况。设定合适的阈值,只要检测到在任何一个方向上顶点邻接面法向量的变化超过阈值,该顶点即被识别为特征点。然后,针对现有网格模型特征识别算法无法检测三维医学模型普遍存在的一种仅沿z轴方向分布的梯田型结构的问题,单独探测医学模型网格顶点邻接面法向量沿z轴方向变化的情况,将变化超出阈值的顶点识别为梯田型结构顶点,正确地将非正常梯田型结构从人体模型正常结构特征中分离出来。与二面角法的对比实验的结果显示：在相同阈值设置下,所提方法能更好地识别出网格模型特征,解决了二面角法在没有明显折线的平滑区域上无法有效识别特征点的问题;同时,也解决了现有网格模型特征检测算法因不具备方向探测能力而无法将医学模型非正常梯田型结构与正常人体结构区分开来的问题,为医学模型后续数字几何处理工作提供了条件。     

Intelligent finite element mesh generation

A knowledge-based and automatic finite element mesh generator (INTELMESH) for two-dimensional linear elasticity problems is presented. Unlike other approaches, the proposed technique incorporates the information about the object geometry as well as the boundary and loading conditions to generate an a priori finite element mesh which is more refined around the critical regions of the problem domain. INTELMESH uses a blackboard architecture expert system and the new concept of substracting to locate the critical regions in the domain and to assign priority and mesh size to them. This involves the decomposition of the original structure into substructures (or primitives) for which an initial and approximate analysis can be performed by using analytical solutions and heuristics. It then uses the concept of wave propagation to generate graded nodes in the whole domain with proper density distribution. INTELMESH is fully automatic and allows the user to define the problem domain with minimum amount of input such as object geometry and boundary and loading conditions. Once nodes have been generated for the entire domain, they are automatically connected to form well-shaped triangular elements ensuring the Delaunay property. Several examples are presented and discussed. When incorporated into and compared with the traditional approach to the adaptive finite element analysis, it is expected that the proposed approach, which starts the process with near optimal initial meshes, will be more accurate and efficient.     

The Cut&Glue mesh generation algorithm

This paper describes a technique for generating quadrilateral finite element meshes on convex, four-sided patches, given an arbitrary number of elements along each side of the patch. The technique first generates a subdivision with the correct topological structure and smoothes the subdivision to obtain elements of acceptance shape for finite element analysis. The correct mesh topology is obtained from a regular subdivision by cutting rectangular corners of appropriate size and interconnecting the sides introduced by the cuts.The method can also be applied on three-dimensional patches producing meshes of brick elements with gradations in all directions.     

Automatic hexahedral mesh generation using a new grid-based method with geometry and mesh transformation

A geometry and mesh transformation approach is proposed to overcome the traditional problem of poorly shaped elements at the boundary using the grid-based method of mesh generation. This is achieved by transforming the original geometric model to a topologically similar recognition model which conforms fully to the Cartesian directions. Such a recognition model is constructed by tessellating the original model and then employing a fuzzy logic method to determine the normal directions of the faces. A three-dimensional field morphing algorithm is used to position the features of the recognition model. Such a recognition model is then meshed with hexahedral elements without any degeneracy using the new grid-based algorithm. The mesh of the recognition model is mapped back to the original geometric model by employing a transformation based on the Laplacian-isoparametric equation.     

Matching interior and exterior all-quadrilateral meshes with guaranteed angle bounds

This paper presents an extension of our earlier work on quadtree-based all-quadrilateral mesh generation, which generates guaranteed-quality meshes for the interior or exterior domain of any given planar curve. In this paper, we develop an algorithm to match the generated interior and exterior meshes with conformal boundary, preserving the guaranteed angle bounds. In addition, we introduce another automatic and robust approach to preserve sharp features. All the elements in the final mesh are within $[45^{\circ} - \varepsilon, 135^{\circ} + \varepsilon] (\varepsilon \leq 5^{\circ}),$ except small sharp angles present in the input geometry. Here, $\varepsilon$ is an input parameter. The smaller $\varepsilon$ is, the better angle bounds we can get. Finally, we group all the elements into six types, and most elements only need a few flops to construct the element stiffness matrix. This will significantly reduce the computational time during the finite element analysis.     

Boosting image caption generation with feature fusion module

Multimedia Tools and Applications - Image caption generation has been considered as a key issue on vision-to-language tasks. Using the classification model, such as AlexNet, VGG and ResNet as the...     

As-rigid-as-possible mesh deformation and its application in hexahedral mesh generation

This paper presents an efficient and stable as-rigid-as-possible mesh deformation algorithm for planar shape deformation and hexahedral mesh generation. The deformation algorithm aims to preserve two local geometric properties: scale-invariant intrinsic variables and elastic deformation energy, which are together represented in a quadric energy function. To preserve these properties, the position of each vertex is further adjusted by iteratively minimizing this quadric energy function to meet the position constraint of the controlling points. Experimental results show that the deformation algorithm is efficient, and can obtain physically plausible results, which have the same topology structure with the original mesh. Such a mesh deformation method is useful to project the source surface mesh onto the target surfaces in hexahedral mesh generation based on sweep method, and application results show that the proposed method is feasible to mesh projection not only between similar surface contours but also dissimilar surface contours.