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。     

基于圆形参数域和重要性采样的三维模型网格重建

给出了一个基于参数化和重要性采样的网格重建算法.算法搜索一条切线将三维模型表面切分成一片碟形表面,并将其参数化到二维单位圆中.根据模型的曲率信息和参数化的扭曲度生成一张控制图.利用蓝噪声采样算法对用控制图调制后的采样密度采样得到离散采样点.通过对采样点进行平面三角化并将其映射回三维空间实现了三维网格重建.实验证明,该方法有效地改善了参数化的扭曲度,并能得到具有自适应性的高度规则网格.     

自适应三角网格模型重新布点算法的研究

在对任意拓扑三角网格模型进行自动三边界区域划分的基础上，提出一种适应的三角网格模型重新布点算法，该算法首先根据三边界区域划分的结果，构造初始网格模型具有最低分辨率的基础网格模型，然后利用协调映射技术，对网格模型进行重新采样，从而不断对基础网格模型进行细化，算法的特点是可以根据不同的精度自动在曲面的大曲率处重新采样得到较多的点，而在曲面的小曲率处则重新采样得到较少的点，该算法可以用于三角网模型的自适应简化和优化，文中的应用实例表明，该算法可以保证在满足指定精度要求的条件下，得到更合理的三角网格模型，取得理想的效果。     

基于隐函数插值的连续多分辨率模型

提出了一种基于变分隐函数插值的连续多分辨率模型生成算法,通过递归地删除网格模型中的边得到连续的简化模型.算法采用变分隐函数插值的方法对网格模型分区域插值,生成原始模型的区域插值隐函数曲面,并以对应隐函数曲面上的采样点作为边折叠的目标点.算法建立了可调加权控制函数来控制边的简化顺序.在模型简化过程中,可通过交互调节控制函数的权值执行不同的简化原则,使得重要度低的边优先删除.此外,通过建立独立集,避免了模型的局部过度简化.实验结果表明,此算法能实现较理想的简化效果.     

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.     

边界优先的Delaunay-层推进曲面四边形网格生成

为了提高复杂组合曲面四边形网格生成的鲁棒性和边界单元质量,提出一种边界优先的Delaunay-层推进网格生成方法.首先在剖分域内粗的约束Delaunay背景网格的辅助下,以物理域的位置偏差为引导,在参数域中迭代计算边界点的法矢量;然后结合层推进策略,在几何特征附近生成各向异性或各向同性正交网格;最后使用Coring技术加速内部网格的生成并进行单元合并,得到四边形为主的网格.若干复杂平面区域和组合曲面模型的剖分结果表明,所提方法可生成等角扭曲度和纵横比优于主流商业软件的网格;在12个线程的PC平台上,使用OpenMP并行剖分包含21 772张曲面的引擎模型只用了38.68 s.     

基于曲率流的四边形主导网格的光顺方法

网格模型是计算机图形学和数字几何处理中运用最为广泛的三维几何表达方式.四边网格(以四边形为主的网格)由于其符合人们对几何形状变化的自然感知,在表示三维几何上有其独有的优势,并且可以更为直接地应用在几何造型、细分曲面、建筑设计等方面.文中针对四边形主导网格含有噪声的情况,设计了一种基于表面微分属性的光顺方法,该方法具有易实现、计算效率高的特点.基于曲率流的几何扩散可以有效地保持原网格的几何特征,同时还针对四边形主导网格的T-顶点进行了特殊处理.     

基于距离场的三维模型网格重建

根据任意亏格和任意边界的3D网格模型,给出一种网格重建算法。该算法通过对原始网格进行一系列自适应的局部修改操作,改进网格中三角形的质量和顶点位置分布。为减少优化过程中误差的累积,提出基于距离场的算法将新生成的顶点保留到原始网格曲面上,该算法实现简单,不需要复杂的全局参数化操作。实验结果表明,该算法有效、快速、稳定。     

非结构化四边形网格生成新算法

改进了一类基于递归区域分解过程的四边形网格生成算法。引入一套健壮的网格模板,为子域的网格剖分提供统一的处理方案,不再限制最终子域为4节点、6节点或8节点子域,提高了算法的时空效率。结合新的子域网格生成过程和自动区域分解算法,利用背景网格和网格源控制分解线上点的布置,得到一个全自动的非结构化四边形网格生成算法。最后通过网格及数值模拟实例验证了算法性能和实用性。     

基于STL三角网格模型简化的研究

针对STL三角网格模型简化中的相关问题进行了研究,并设计出了相应的算法.三角网格的简化过程包括网格删除和网格重建两个过程,在网格的删除中,根据设定的三角形的权重阚值选择删除被删除的三角形区域.在网格重建中,任意选择重建区域的一个顶点,通过渐进收缩的方式,将新生成的三角形边构造一个平衡二叉树,再以三角网格的适应度和平滑度为依据,找出所有二又树中最佳的分支,使重建的三角网格最优化.对两个实例进行探讨,实现对不同STL三角网格的验证,并以原始网格模型与简化后的网格模型进行对比,表明研究所得的简化网格模型既有效地实现了STL网格模型的简化,又保持了原有STL网格模型的基本特征,达到令人满意的结果.     

Retiling scheme: a novel approach of direct anisotropic quad-dominant remeshing

Remeshing has been an active research topic in Digital Geometry Processing. In this paper, a novel approach of direct anisotropic quad-dominant remeshing is proposed. We apply the retiling method to the particular problem of quad-dominant remeshing. Compared with other methods, this method can simply partition the surface of an original triangular mesh into connected quads with the mesh edges aligning to the principal directions. The first step in this method is to estimate and smooth the curvature tensor field of the surface at the vertices, and then the quad-dominant mesh is obtained by retiling the quad surface so that quadrilateral edges are parallel to the local principal curvature directions. In addition, to preserve the sharp feature information during remeshing processes, the feature lines can be extracted using mesh segmentation method, and the intersections between the feature lines and the orthogonal planes can be found during the process of retiling. A feature fusion process is presented to join the feature edges and feature points into the quad-dominant mesh. The experiment results show that this new remeshing method is simple and easy to implement. The resolution of the quadrilateral mesh can be controlled during the remeshing. It is applicable to arbitrary genus meshes and can generate high-quality quad-dominant mesh.     

An effective quad-dominant meshing method for unorganized point clouds

To perform quad meshing on raw point clouds, existing algorithms usually require a time-consuming parameterization or Voronoi space partition process. In this paper, we propose an effective method to generate quad-dominant meshes directly from unorganized point clouds. In the proposed method, we first apply Marinov’s curvature tensor optimization to the input point cloud to reduce the umbilical regions in order to obtain a smooth curvature tensor. We then propose an efficient marching scheme to extract the curvature lines with controllable density from the point cloud. Finally, we apply a specialized K-Dimension (KD) tree structure, which converts the nearest neighbor searching problem into a sorting problem, to efficiently estimate the intersections of curvature lines and recover the topology of the quad-dominant meshes. We have tested the proposed method on different point clouds. Our results show that the proposed method produces good quality meshes with high computational efficiency and low memory requirement.     

Anisotropic Filtering of Non-Linear Surface Features

A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non‐linear geometric features such as curved surface regions and feature lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operator and principal curvature properties on simplicial surfaces that is fully consistent with the well‐known discrete mean curvature formula, 2. an anisotropic discrete mean curvature vector that combines the advantages of the mean curvature normal with the special anisotropic behaviour along feature lines of a surface, and 3. an anisotropic prescribed mean curvature flow which converges to surfaces with an estimated mean curvature distribution and with preserved non‐linear features. Additionally, the PMC flow prevents boundary shrinkage at constrained and free boundary segments.     

Detection of Salient Curvature Features on Polygonal Surfaces

We develop an approach for stable detection of perceptually salient curvature features on surfaces approximated by dense triangle meshes. The approach explores an "area degenerating" effect of the focal surface near its singularities and combines together a new approximations of the mean and Gaussian curvatures, nonlinear averaging of curvature maps, histogram-based curvature extrema filtering, and an image processing skeletonization procedure adapted for triangular meshes. Finally we use perceptually significant curvature extrema triangles to enhance the Garland-Heckbert mesh decimation method.     

Sampling framework for accurate curvature estimation in discrete surfaces

Accurate curvature estimation in discrete surfaces is an important problem with numerous applications. Curvature is an indicator of ridges and can be used in applications such as shape analysis and recognition, object segmentation, adaptive smoothing, anisotropic fairing of irregular meshes, and anisotropic texture mapping. In this paper, a new framework is proposed for accurate curvature estimation in discrete surfaces. The proposed framework is based on a local directional curve sampling of the surface where the sampling frequency can be controlled. This local model has a large number of degrees of freedoms compared with known techniques and, so, can better represent the local geometry. The proposed framework is quantitatively evaluated and compared with common techniques for surface curvature estimation. In order to perform an unbiased evaluation in which smoothing effects are factored out, we use a set of randomly generated Bezier surface patches for which the curvature values can be analytically computed. It is demonstrated that, through the establishment of sampling conditions, the error in estimations obtained by the proposed framework is smaller and that the proposed framework is less sensitive to low sampling density, sampling irregularities, and sampling noise.     

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.     

曲面的自适应三角网格剖分

在传统的映射法基础上 ,采用自适应三角网格加密法能有效地处理带有特征约束条件的任意曲面的三角剖分问题 .在平面三角化算法中对环边统一处理 ,并且采取了一种简单有效的曲率估算方法 ,提高了运行效率 ;并在保持外观的基础上进行了网格质量的优化     

反向工程中三角网格的加工特征识别

为实现反向工程中的特征重构,提出一种在三角网格上由Morse-Smale复形转换为分割面属性邻接图进行加工特征提取的算法.首先通过移动最小二乘曲面法计算网格顶点曲率,构建曲率特性指标函数,消除因网格连接引起的误差,达到降噪的作用;然后在三角网格上建立和简化Morse-Smale复形,精确提取特征线,将网格分割为边界清晰连续的区域,并获得各区域的邻接关系;最后判断关键点和特征线的性质,将Morse-Smale复形直接转换为分割面属性邻接图进行加工特征识别.实验结果表明,该算法准确、高效,而且不需要人工干预,对于反向工程中大规模、带噪声的网格具有较好的识别效果.     

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。