由区域生长算法实现四边形网格划分

针对当前各种三角形网格转化为四边形网格算法的缺陷，提出一种实现这种转化的算法——区域生长算法．该算法通过有选择地合并三角形来获得高质量的四边形网格，并且对两个三角形的合并增加约束条件以避免在生成四边形网格的过程中产生残余三角形；同时对生成的四边形网格进行一系列的质量改善操作。     

四边形有限元网格的快速生成算法

给出一个使用覆盖栅格生成四边形网格的算法．覆盖法能够快速生成有限元网格，但是边界单元的质量通常比较差，也难以得到全部的四边形网格．将边界内角分成4类，根据不同类型的内角，提出相应的使用覆盖栅格生成完全四边形网格所要采取的修正措施．最后，应用文中算法进行网格划分，结果表明该算法是有效的．     

建筑结构模型的四边形网格生成算法

为提高建筑结构有限元分析计算的效率,提出建筑结构模型的四边形网格生成算法．首先采用改进的折半查找算法快速建立相应的结构模型索引信息;然后根据四边形网格划分的原则调整模型边界;最后采用分区域模板法对整体结构模型进行四边形网格的自动生成．算例表明该算法可以根据有限元分析计算中模型的特点简化模型,降低计算时间．     

四边形网格生成中的前沿边生长改进算法

为提高B样条曲面重构中点云四边形网格的生成效率和质量,对现有的四边形网格Q-Morph前沿边生长算法进行改进,提出面向四边形网格生成的三角网格拓扑优化方法,通过设定生长限制条件和调整网格顶点度,保证全局四边形网格质量,实现适合复杂曲面重构的规则四边形网格获取。实例结果表明,该算法效率高、适应性好,生成的四边形网格具有分布均匀、不规则网格数量少的优点。     

基于C—C细分的四边形网格上插值光滑Bezier曲面的生成

在任意拓扑的四边形网格上构造光滑的曲面是计算机辅助几何设计中的一个重要问题．基于C—C细分,提出一种从四边形网格上生成插值网格顶点的光滑Bezier曲面片的算法．将输入四边形网格作为C—C细分的初始控制网格,在四边形网格的每张面上对应得到一张Bezier曲面,使Bezier曲面片逼近C—C细分极限曲面．曲面片在与奇异顶点相连的边界上G^1连续,其他地方C^2连续．为解决C—C细分的收缩问题,给出了基于误差控制的迭代扩张初始控制网格的方法,使从扩张后网格上生成的曲面插值于初始控制网格的顶点．实验结果表明,该算法效率高,生成的曲面具有较好的连续性,适用于对四边化后的网格模型上重建光滑的曲面．     

四边形网格的去边细分方法

提出一种四边形网格细分算法：每细分一次四边形网格，其数目增加为原来的两倍，细分二次结果相当于一次二分细分和一个旋转．该算法采用三次B样条张量积的形式，其生成曲面在规则点具有C^2连续性，在非规则点具有C^1连续性．由于该细分算法对网格几何操作简单，所得网格数据量增长相对缓慢，适合于3D图像重构及网络传输等应用领域。     

带 2细分结构的四边形化

在Morse函数理论的基础上,提出一种新的从三角网格中建立四边形网格多分辨率表示的方法．先由人工指定或从拉普拉斯矩阵的特征函数中提取临界点,计算带约束的拉普拉斯方程得到光滑的Morse函数．函数的临界点（极大、极小和鞍点）有规律地分布在模型表面,在三角网格表面梯度场的引导下, 生成临界点间流线,得到临界点间的拓扑关系．通过临界点交换规则,同样是采用流线的方法,得到更精细的四边形网格。 最终可实现无需参数化而仅用流线方法来建立不同多分辨率表示的四边形网格。     

三角形网格转化为四边形网格

现有的全自动网格划分算法大部分生成三角形网格。生成四边形网格更困难。为了缓解这个问题，本文研究并实现了三角形网格转化为四边形网格的线性算法。该算法是对已有的Ｏ（Ｎ＾２）算法的改进。     

多面约束棱台体全六面体网格生成算法

利用四角点双线性插值反映射法确定两多边域间的映射点；运用约束引导线和节点等参光顺法实现对多边形的四边形分解；最后，结合超限映射法与分层原则实现该类实体全六面体有限元网格生成．文中算法拓广了超限映射法的应用范围．实例表明：该算法简单、效率高、生成单元的质量好。     

四边形网格优化中的螺旋条带生成

已有的四边形网格的简化及优化方法大多数都是三角形网格简化在局部几何上的推广.四边形网格的结构受螺旋条带的影响,移除四边形网格中的螺旋条带则可以在拓扑结构上明显提高四边形网格的质量.文中具体讨论了四边形网格上螺旋条带与网格上奇异点的关系及其性质,并根据这个性质给出了四边形网格中螺旋条带的一般生成算法.实验结果表明,该算法可以有效地搜索四边形网格上的螺旋条带,进而通过删除螺旋条带优化四边形网格的拓扑结构.     

边界特征保持的网格模型分级二次误差简化算法

在参考张量投票理论的基础上,结合二次误差简化算法,提出一种边界特征保持的几何网格模型分级二次误差简化算法.首先根据张量投票理论对三角网格顶点进行面点、边点、角点类型分类;然后对各边对按照二次误差简化算法进行边折叠代价计算;再将分类顶点按照设定的等级权重加入边对折叠代价中,从而保证渐进式简化过程中能够对顶点进行分级简化.实验结果表明,该算法不但能实现渐进简化,而且能按需保留模型的整体特征和细节特征.     

QuadriFlow: A Scalable and Robust Method for Quadrangulation

QuadriFlow is a scalable algorithm for generating quadrilateral surface meshes based on the Instant Field‐Aligned Meshes of Jakob et al. (ACM Trans. Graph. 34(6):189, 2015). We modify the original algorithm such that it efficiently produces meshes with many fewer singularities. Singularities in quadrilateral meshes cause problems for many applications, including parametrization and rendering with Catmull‐Clark subdivision surfaces. Singularities can rarely be entirely eliminated, but it is possible to keep their number small. Local optimization algorithms usually produce meshes with many singularities, whereas the best algorithms tend to require non‐local optimization, and therefore are slow. We propose an efficient method to minimize singularities by combining the Instant Meshes objective with a system of linear and quadratic constraints. These constraints are enforced by solving a global minimum‐cost network flow problem and local boolean satisfiability problems. We have verified the robustness and efficiency of our method on a subset of ShapeNet comprising 17,791 3D objects in the wild. Our evaluation shows that the quality of the quadrangulations generated by our method is as good as, if not better than, those from other methods, achieving about four times fewer singularities than Instant Meshes. Other algorithms that produce similarly few singularities are much slower; we take less than ten seconds to process each model. Our source code is publicly available.     

Improving the Quality of Conforming Triangular Meshes by Topological Clean up and DSI

A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. This method can improve the angle distribution of mesh element. while keeping the resulting meshes conform to the predefined constraints which are inputted as a PSLG.1 Introduction Triangular mesh is very useful in manyapplications, especially in numerical simulationssuch as finite elem…     

Localized coarsening of conforming all-hexahedral meshes

Finite element mesh adaptation methods can be used to improve the efficiency and accuracy of solutions to computational modeling problems. In many applications involving hexahedral meshes, localized modifications which preserve a conforming all-hexahedral mesh are desired. Effective hexahedral refinement methods that satisfy these criteria have recently become available; however, due to hexahedral mesh topology constraints, little progress has been made in the area of hexahedral coarsening. This paper presents a new method to locally coarsen conforming all-hexahedral meshes. The method works on both structured and unstructured meshes and is not based on undoing previous refinement. Building upon recent developments in quadrilateral coarsening, the method utilizes hexahedral sheet and column operations, including pillowing, column collapsing, and sheet extraction. A general algorithm for automated coarsening is presented and examples of models that have been coarsened with this new algorithm are shown. While results are promising, further work is needed to improve the automated process.     

结合边折叠和局部优化的网格简化算法

针对目前网格简化算法在将三维模型简化到较低分辨率时,网格模型的细节特征丢失、网格质量不佳的问题,提出一种保持特征的高质量网格简化算法。引入顶点近似曲率的概念,并将其与边折叠的误差矩阵结合,使得简化模型的细节特征在最大限度上得到保持。同时分析简化后三角网格的质量,对三角网格作局部优化处理,减少狭长三角形的数量,提高简化模型的网格质量。使用Apple模型和Horse模型进行实验,并与一种经典的基于边折叠的网格简化算法以及其改进算法之一进行对比。实验结果显示,两种对比算法三角网格分布过于均匀,局部细节模糊不清,而所提算法的三角网格在曲率大的区域稠密,在平坦处稀疏,细节特征清晰可辨;简化模型的几何误差的数量值与两种对比算法处于同一数量级;所提算法的简化网格的平均质量远高于两种对比算法。实验结果表明,在不扩大几何误差的情况下,所提算法不仅具有较强的细节特征保持能力,而且简化模型的网格质量较高,视觉效果较好。     

蒙太奇网格融合

三维物体融合是一种新的几何造型方法,它利用三维模型之间的剪贴操作从两个或多个现有的几何模型中光滑融合出新的几何模型.提出了一种基于局部调和映射的三维网格蒙太奇融合新方法.首先利用网格上的近似等距线算法来抽取出待融合区域,然后对两个待融合区域进行带内孔的调和映射参数化,最后通过拓扑合并和融合控制来实现网格的光滑融合.与原有的基于全局调和映射的融合方法相比,新方法的算法效率大幅度提升,求解时间不再随融合模型顶点数的增加而呈指数增长;减少了二维网格拓扑合并中奇异情况出现的概率,提高了算法的稳定性;被剪切网格的细节得到完整保留;消除了原算法对融合区域拓扑的限制.实验结果表明,此方法可以用来生成许多三维动画中的特殊夸张造型效果,在影视动画中具有应用价值.     

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.     

Calculation of gas flow parameters around a reentry vehicle

An original numerical algorithm for calculating the gas parameters around a reentry vehicle was described and tested. It is based on a system of Quasi Gas Dynamics (QGD) equations and its approximations on hybrid meshes, which suppose adaptive, locally thickening meshes including both rectangular and triangular cells. The results of the calculations on a sequence of condensed meshes for Mach number values of 2, 5, and 12 are presented. These results correspond to well-known data and demonstrate the high efficiency of the algorithm.     

求解背包问题的改进差异演化算法

提出一种求解0-1背包问题的改进差异演化算法。首先对差异演化算法的选择操作进行修改,得到的改进差异演化算法可以直接有效地处理约束优化问题。其次,利用一种新的区间编码映射机制,将差异演化算法扩展到求解离散领域优化问题。仿真实验结果表明,与其他进化算法相比,改进差异演化算法求解经典背包问题时,求解精度高,收敛速度快,是求解经典背包问题的一种高效算法。     

Wavelet-based multiresolution analysis of irregular surface meshes

We extend Lounsbery's multiresolution analysis wavelet-based theory for triangular 3D meshes, which can only be applied to regularly subdivided meshes and thus involves a remeshing of the existing 3D data. Based on a new irregular subdivision scheme, the proposed algorithm can be applied directly to irregular meshes, which can be very interesting when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. This is very convenient in CAD (computer-assisted design), when the mesh has attributes such as texture and color information, or when the 3D mesh is used for simulations, and where a different connectivity could lead to simulation errors. The algorithm faces an inverse problem for which a solution is proposed. For each level of resolution, the simplification is processed in order to keep the mesh as regular as possible. In addition, a geometric criterion is used to keep the geometry of the approximations as close as possible to the original mesh. Several examples on various reference meshes are shown to prove the efficiency of our proposal.