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.     

平面任意区域四边形网格自动生成的一种方法

在改进节点连接法的基础上，提出了一种平面任意区域的有限元网格全自动剖分方法，既能快速生成四边形单元网格，也能生成三角形单元网格；     

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．     

四边形与六面体自动重网格化技术研究综述EI北大核心CSCD

四边形、六面体网格具有良好的局部单元特性和整体拓扑性质,其在几何处理、有限元计算等大量的应用中有着不可替代的优势.然而,这些应用对所生成的网格有很高的要求,如要求较低的形状误差、较高的单元质量、较少的单元格数、较优的拓扑结构等.这些要求对生成符合特定应用需求的网格提出了巨大的挑战.这些要求之间存在冲突和制约,因而很难获得满足所有要求的网格.生成符合特定应用需求的这种网格有着巨大的挑战.文中从流形网格参数化的视角,系统地介绍近些年来典型的自动优化方法,分析相关技术的优缺点,讨论并给出了当前面临的主要技术挑战和今后发展方向.     

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。     

全局各向异性四边形主导网格重建方法

四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡.为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格.重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样;再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除;如此循环,直至达到理想的采样密度.该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征.同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格.     

前沿法生成四边形网格的改进方法

针对传统前沿法生成四边形网格时算法不稳定,有残余三角形等缺点,该文提出泛前沿的概念。泛前沿是对目前前沿概念的更高层次上的抽象,不但避免了前沿拆分和合并带来的不稳定,而且使得前沿操作起来更简单有效。然后文章通过消除坏四边形单元,消除残余三角形单元等操作,最终得到了质量较好的全四边形网格。最后,给出了用此法划分的例子。     

非封闭曲面的海量空间数据点四边形网格生成算法

从数据模型的任意一点开始选择一个初始的四边形网格单元,采用动态边界边扩展的方法在三维空间直接进行四边形网格划分;在网格划分过程中实现了边界冲突检测、网格顶点优化处理、网格边界处理和网格综合优化.最后给出了网格生成实例.实验结果表明:该算法生成的网格质量较好,运行速度较快.     

二维域多约束四边形有限元网格生成算法

以Q-Morph算法思想为基础,实现增加约束后自动生成二维域多约束四边形有限元网格．通过增加约束修补子算法,使原算法思想适用于附加的多约束;同时调整了原有算法中单元四边形顶边的生成子算法和四边形内多余三角形删除子算法的烦琐之处．实例测试结果表明,用文中算法生成的约束四边形网格具有网格分布较均匀、网格形状较规整等特点．     

边界简化与多目标优化相结合的高质量四边形网格生成

目的 高质量四边形网格生成是计算机辅助设计、等几何分析与图形学领域中一个富有挑战性的重要问题。针对这一问题,提出一种基于边界简化与多目标优化的高质量四边形网格生成新框架。方法 首先针对亏格非零的平面区域,提出一种将多连通区域转化为单连通区域的方法,可生成高质量的插入边界;其次,提出"可简化角度"和"可简化面积比率"两个阈值概念,从顶点夹角和顶点三角形面积入手,将给定的多边形边界简化为粗糙多边形;然后对边界简化得到的粗糙多边形进行子域分解,并确定每个子域内的网格顶点连接信息;最后提出四边形网格的均匀性和正交性度量目标函数,并通过多目标非线性优化技术确定网格内部顶点的几何位置。结果 在同样的离散边界下,本文方法与现有方法所生成的四边网格相比,所生成的四边网格顶点和单元总数目较少,网格单元质量基本类似,计算时间成本大致相同,但奇异点数目可减少70% 80%,衡量网格单元质量的比例雅克比值等相关指标均有所提高。结论 本文所提出的四边形网格生成方法能够有效减少网格中的奇异点数目,并可生成具有良好光滑性、均匀性和正交性的高质量四边形网格,非常适用于工程分析和动画仿真。     

Topological improvement procedures for quadrilateral finite element meshes

This paper presents a set of procedures for improving the topology of unstructured quadrilateral finite element meshes. These procedures are based on the topology of the finite element mesh, and all operations act only on local regions of the mesh. The goal is to optimize the topology such that the smoothing process can produce the best possible element quality. Topological improvement procedures are presented both for elements that are interior to the mesh and for elements connected to the boundary. Also presented is a discussion of efficiency and optimal ordering of the procedures. Several example meshes are included to show the effectiveness of the current approach in improving element qualities in a finite element mesh.     

Topological refinement procedures for triangular finite element meshes

This paper presents a topological approach to improve the quality of unstructured triangular finite element meshes. Topological improvement procedures are presented both for elements that are interior to the mesh and for elements connected to the boundary. Optimal ordering of the topology improvement operations and their efficient implementation is also discussed. Several example meshes are included to demonstrate the effectiveness of the approach in improving element quality in a finite element mesh.     

GEncode: Geometry-driven compression for General Meshes

Performances of actual mesh compression algorithms vary significantly depending on the type of model it encodes. These methods rely on prior assumptions on the mesh to be efficient, such as regular connectivity, simple topology and similarity between its elements. However, these priors are implicit in usual schemes, harming their suitability for specific models. In particular, connectivity‐driven schemes are difficult to generalize to higher dimensions and to handle topological singularities. GEncode is a new single‐rate, geometry‐driven compression scheme where prior knowledge of the mesh is plugged into the coder in an explicit manner. It encodes meshes of arbitrary dimension without topological restrictions, but can incorporate topological properties, such as manifoldness, to improve the compression ratio. Prior knowledge of the geometry is taken as an input of the algorithm, represented by a function of the local geometry. This suits particularly well for scanned and remeshed models, where exact geometric priors are available. Compression results surfaces and volumes are competitive with existing schemes.     

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.     

散乱数据点的增量快速曲面重建算法

给出了一个新的散乱数据的曲面重建算法.算法充分利用邻近点集反映出的局部拓扑和几何信息,基于二维Delaunay 三角剖分技术快速地实现每个数据点的局部拓扑重建,然后通过自动矫正局部数据点的非法连接关系,以增量扩张的方式把局部三角网拼接成一张标准的整体二维流形网格.该算法在重建过程中能自动进行洞的检测,判断出散乱数据所蕴涵的开或闭的拓扑结构.实验结果表明,该算法高效、稳定,可以快速地直接重构出任意拓扑结构的二维流形三角形网格.     

ParTopS: compact topological framework for parallel fragmentation simulations

Cohesive models are used for simulation of fracture, branching and fragmentation phenomena at various scales. Those models require high levels of mesh refinement at the crack tip region so that nonlinear behavior can be captured and physical results obtained. This imposes the use of large meshes that usually result in computational and memory costs prohibitively expensive for a single traditional workstation. If an extrinsic cohesive model is to be used, support for dynamic insertion of cohesive elements is also required. This paper proposes a topological framework for supporting parallel adaptive fragmentation simulations that provides operations for dynamic insertion of cohesive elements, in a uniform way, for both two- and three-dimensional unstructured meshes. Cohesive elements are truly represented and are treated like any other regular element. The framework is built as an extension of a compact adjacency-based serial topological data structure, which can natively handle the representation of cohesive elements. Symmetrical modifications of duplicated entities are used to reduce the communication of topological changes among mesh partitions and also to avoid the use of locks. The correctness and efficiency of the proposed framework are demonstrated by a series of arbitrary insertions of cohesive elements into some sample meshes.     

A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes

Large-scale simulation of separation phenomena in solids such as fracture, branching, and fragmentation requires a scalable data structure representation of the evolving model. Modeling of such phenomena can be successfully accomplished by means of cohesive models of fracture, which are versatile and effective tools for computational analysis. A common approach to insert cohesive elements in finite element meshes consists of adding discrete special interfaces (cohesive elements) between bulk elements. The insertion of cohesive elements along bulk element interfaces for fragmentation simulation imposes changes in the topology of the mesh. This paper presents a unified topology-based framework for supporting adaptive fragmentation simulations, being able to handle two- and three-dimensional models, with finite elements of any order. We represent the finite element model using a compact and “complete” topological data structure, which is capable of retrieving all adjacency relationships needed for the simulation. Moreover, we introduce a new topology-based algorithm that systematically classifies fractured facets (i.e., facets along which fracture has occurred). The algorithm follows a set of procedures that consistently perform all the topological changes needed to update the model. The proposed topology-based framework is general and ensures that the model representation remains always valid during fragmentation, even when very complex crack patterns are involved. The framework correctness and efficiency are illustrated by arbitrary insertion of cohesive elements in various finite element meshes of self-similar geometries, including both two- and three-dimensional models. These computational tests clearly show linear scaling in time, which is a key feature of the present data-structure representation. The effectiveness of the proposed approach is also demonstrated by dynamic fracture analysis through finite element simulations of actual engineering problems.

Carving for topology simplification of polygonal meshes

The topological complexity of polygonal meshes has a large impact on the performance of various geometric processing algorithms, such as rendering and collision detection algorithms. Several approaches for simplifying topology have been discussed in the literature. These methods operate locally on models, which makes their effect on the topology hard to predict and analyze. Most existing methods tend to exhibit several disturbing artifacts, such as shrinking of the input and splitting of its components. We propose a novel top-down approach for topology simplification that avoids most problems that are common in existing methods. We start with a simple, genus-zero mesh that bounds the input and gradually introduce topologic features by a series of carving operations. This process yields a multiresolution stream of meshes with increasing topologic level of detail. We further present a carving algorithm that is based on constrained Delaunay tetrahedralization. The algorithm first constructs the tetrahedral mesh of the complement of the input with respect to its convex hull. It then proceeds to eliminate tetrahedra in a prioritized manner. We present quality results for two families of meshes that are difficult to simplify by all existing methods known to us: topologically complex meshes and highly clustered meshes.     

A diffusion wavelet approach for 3-D model matching

This paper proposes a new 3D shape retrieval approach based on diffusion wavelets which generalize wavelet analysis and associated signal processing techniques to functions on manifolds and graphs. Unlike current works on 3D matching, which are based either on the topological information of the model or its scatter point distribution information, this approach uses both information for more effective matching. Diffusion wavelets enable both global and local analyses on graphs, and can capture the topology of a surface with the diffusion map of its mesh representation. As a result, both multi-scale properties of the 3D geometric model and the topology among the meshes can be extracted for use in 3D geometric model retrieval. Tests using 3D benchmarks demonstrate that the approach based on diffusion wavelets is effective and performs better than those by spherical wavelet and spherical harmonics in 3D model matching.     

Towards modelling of a trabecular bone

Trabecular bone (lightweight spongy bone) comprises of a complex arrangement of plates and struts at micro level that make it anisotropic. Osteoporosity (leading to fracture) is a common problem in old age which makes the bone weak due to increased porosity. Considerable two dimensional data in the form of images is available on the porous structure of the bone, however this needs to be related to the macro-level anisotropic properties. This preliminary study aims to examine whether topological anisotropy can be related to elastic anisotropy. Simple three dimensional structured meshes comprising of elements with different material properties are used to simulate the porous structure. Homogenised elastic properties are evaluated and these are compared with a two dimensional topology anisotropy indicators. For the simple problems considered it appears that topological anisotropy cannot be directly linked to elastic anisotropy.