参数平面二叉树剖分网格简化

为了快速地对3维网格模型进行简化,提出了一种曲率自适应的3维网格简化算法,该算法首先将原始网格投影至参数平面上,并构造反映原始网格曲率分布的平面曲率灰度分布,用以表征简化过程中对网格各部分不同的采样密度要求;然后根据等曲率灰度分割的原则来对参数平面进行二叉树剖分,以构造反映其不均匀分布的非均衡二叉树结构,并依此选取简化后的网格顶点集合,以构造简化的三角网格.该算法的优点是执行速度快,同时在简化过程中仍能充分保持原始网格的细节.     

基于边折叠和质点-弹簧模型的网格简化优化算法

通过边折叠实现网格曲面简化，提出了保持曲面特征的边折叠基本规则，引入边折叠顺序控制因子λ，给出了折叠点坐标获取方法，简化过程中网格边长度趋于均匀．在曲面简化基础上，利用质点-弹簧模型优化网格形状．将网格顶点邻域参数化到二维域上，在质点-弹簧模型中引入约束弹簧，约束调整网格顶点，并逆映射到三维原始曲面上，局部优化网格顶点的相邻网格；调整曲面上所有网格顶点，在全局上优化网格形状．在曲面简化优化过程中，建立原始模型曲面和简化优化后曲面之间的双向映射关系；曲面的网格顶点始终在原始模型表面上滑动，并以双向Hausdorff距离衡量、控制曲面间的形状误差．应用实例表明：文中算法稳定、高效，适合于任意复杂的二维流形网格．     

Vertex location optimisation for improved remeshing

Remeshing aims to produce a more regular mesh from a given input mesh, while representing the original geometry as accurately as possible. Many existing remeshing methods focus on where to place new mesh vertices; these samples are placed exactly on the input mesh. However, considering the output mesh as a piecewise linear approximation of some geometry, this simple scheme leads to significant systematic error in non-planar regions. Here, we use parameterised meshes and the recent mathematical development of orthogonal approximation using Sobolev-type inner products to develop a novel sampling scheme which allows vertices to lie in space near the input surface, rather than exactly on it. The algorithm requires little extra computational effort and can be readily incorporated into many remeshing approaches. Experimental results show that on average, approximation error can be reduced by 40% with the same number of vertices.     

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。     

5–6–7 Meshes: Remeshing and analysis

We introduce a new type of meshes called 5–6–7 meshes. For many mesh processing tasks, low- or high-valence vertices are undesirable. At the same time, it is not always possible to achieve complete vertex valence regularity, i.e. to only have valence-6 vertices. A 5–6–7 mesh is a closed triangle mesh where each vertex has valence 5, 6, or 7. An intriguing question is whether it is always possible to convert an arbitrary mesh into a 5–6–7 mesh. In this paper, we answer the question in the positive. We present a 5–6–7 remeshing algorithm which converts a closed triangle mesh with arbitrary genus into a 5–6–7 mesh which (a) closely approximates the original mesh geometrically, e.g. in terms of feature preservation and (b) has a comparable vertex count as the original mesh. We demonstrate the results of our remeshing algorithm on meshes with sharp features and different topology and complexity.     

Manifold-guaranteed out-of-core simplification of large meshes with controlled topological type

In this paper, a simple and efficient algorithm is proposed for manifold-guaranteed out-of-core simplification of large meshes with controlled topological type. By dual-sampling the input large mesh model, the proposed algorithm utilizes a set of Hermite data (sample points with normals) as an intermediate model representation, which allows the topological structure of the mesh model to be encoded implicitly and thus makes it particularly suitable for out-of-core mesh simplification. Benefiting from the construction of an in-core signed distance field, the proposed algorithm possesses a set of features including manifoldness of the simplified meshes, toleration of nonmanifold mesh data input, topological noise removal, topological type control and, sharp features and boundary preservation. A novel, detailed implementation of the proposed algorithm is presented, and experimental results demonstrate that very large meshes can be simplified quickly on a low-cost off-the-shelf PC with tightly bounded approximation errors and with time and space efficiency.     

Variational tetrahedral mesh generation from discrete volume data

In this paper, we propose a novel tetrahedral mesh generation algorithm, which takes volumic data (voxels) as an input. Our algorithm performs a clustering of the original voxels within a variational framework. A vertex replaces each cluster and the set of created vertices is triangulated in order to obtain a tetrahedral mesh, taking into account both the accuracy of the representation and the elements quality. The resulting meshes exhibit good elements quality with respect to minimal dihedral angle and tetrahedra form factor. Experimental results show that the generated meshes are well suited for Finite Element Simulations.     

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。     

高精度自适应的四边形网格重建

提出了海量数据点集的四边形网格重建算法。首先根据精度要求简化数据 点,按一定规则连接相邻的简化数据点生成多边形网格,对网格中高斯曲率较大的顶点进行 局部细分提高其精度,然后对多边形网格进行整体细分使其全部转化为四边形网格,最后分 裂度较大的顶点对其进行优化。实验结果表明,算法对拓扑结构较为复杂的海量数据点集的 四边形网格重建是行之有效的。     

Progressive Interpolation based on Catmull‐Clark Subdivision Surfaces

We introduce a scheme for constructing a Catmull‐Clark subdivision surface that interpolates the vertices of a quadrilateral mesh with arbitrary topology. The basic idea here is to progressively modify the vertices of an original mesh to generate a new control mesh whose limit surface interpolates all vertices in the original mesh. The scheme is applicable to meshes with any size and any topology, and it has the advantages of both a local scheme and a global scheme.     

基于检测球控制的网格模型简化算法研究

在逆向工程、计算机图形学等应用领域中,经常采用多边形网格模型(多为三角形网格)来描述几何形体,但网格中三角片数目往往非常庞大.为了保证对模型的后续操作能有效地进行,有必要在满足一定精度的条件下对其进行简化.提出了一种基于检测球控制简化精度的网格模型简化算法.该算法运行速度快,简化效果好.     

Out-of-Core remeshing of large polygonal meshes

We propose an out-of-core method for creating semi-regular surface representations from large input surface meshes. Our approach is based on a streaming implementation of the MAPS remesher of Lee et al. [18]. Our remeshing procedure consists of two stages. First, a simplification process is used to obtain the base domain. During simplification, we maintain the mapping information between the input and the simplified meshes. The second stage of remeshing uses the mapping information to produce samples of the output semi-regular mesh. The out-of-core operation of our method is enabled by the synchronous streaming of a simplified mesh and the mapping information stored at the original vertices. The synchronicity of two streaming buffers is maintained using a specially designed write strategy for each buffer. Experimental results demonstrate the remeshing performance of the proposed method, as well as other applications that use the created mapping between the simplified and the original surface representations.     

Efficiently computing exact geodesic loops within finite steps

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.     

A mesh optimization algorithm based on neural networks

We have developed a mesh simplification method called GNG3D which is able to produce high quality approximations of polygonal models. This method consists of two distinct phases: an optimization phase and a reconstruction phase. The optimization phase is developed by applying an extension algorithm of the growing neural gas model, which constitutes an unsupervised incremental clustering algorithm. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces obtaining the optimized mesh as a result. We study the model theoretically, analyzing its main components, and experimentally, using for this purpose some 3D objects with different topologies. To evaluate the quality of approximations produced by the method proposed in this paper, three existing error measurements are used. The ability of the model to establish the number of vertices of the final simplified mesh is demonstrated in the examples.     

Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains

Semi-regular meshes describe surface models that exhibit a structural regularity that facilitates many geometric processing algorithms. We introduce a technique to construct semi-regular, quad-only meshes from input surface meshes of arbitrary polygonal type and genus. The algorithm generates a quad-only model through subdivision of the input polygons, then simplifies to a base domain that is homeomorphic to the original mesh. During the simplification, a novel hierarchical mapping method, keyframe mapping , stores specific levels-of-detail to guide the mapping of the original vertices to the base domain. The algorithm implements a scheme for refinement with adaptive resampling of the base domain and backward projects to the original surface. As a byproduct of the remeshing scheme, a surface parameterization is associated with the remesh vertices to facilitate subsequent geometric processing, i.e. texture mapping, subdivision surfaces and spline-based modeling.     

An algorithm for LOD by merging near coplanar faces based on gauss sphere

LOD（Level of Detail)models are widely used recently to accelerate the rendering of 3D scenes.An algorithm that creates multiple levels of detail for 3D scene y merging near-coplanar faces is presented in this paper,First a Gauss sphere is defined for the model of scene and it is divided into meshes near-uniformly.Then,the faces of objects are attached to the respective spherical meshes according to their normal direction.If faces attached to the same mesh are connected with each other,they are merged to form a near coplanar patch (Superface),Isolated vertices inside the patch are removed and the patch is retriangulated.To further imporve the simplification,vicinity vertices on the boundary of the surface patch are merged.In the algorithm,a planar separate rule planar-enneatree is adopted to set up a hierarchical structure of the Gauss sphere,which is used to support the hierarchical model of the scene(LOD),the experimental result shows that the algorithm can achieve desired simplification effects.     

一种高效的混合曲面光顺算法

三维扫描技术的发展获得曲面采样数据不再困难,但得到的三角形网格常含有大量噪声。应用顶点分类的方法,提出了一种加权均值滤波与拉普拉斯光顺相结合的混合算法。实验结果表明,该算法既能有效去除噪声,而且很好地保留了原网格模型的特征信息。     

Progressive Lossless Mesh Compression Via Incremental Parametric Refinement

In this paper, we propose a novel progressive lossless mesh compression algorithm based on Incremental Parametric Refinement, where the connectivity is uncontrolled in a first step, yielding visually pleasing meshes at each resolution level while saving connectivity information compared to previous approaches. The algorithm starts with a coarse version of the original mesh, which is further refined by means of a novel refinement scheme. The mesh refinement is driven by a geometric criterion, in spirit with surface reconstruction algorithms, aiming at generating uniform meshes. The vertices coordinates are also quantized and transmitted in a progressive way, following a geometric criterion, efficiently allocating the bit budget. With this assumption, the generated intermediate meshes tend to exhibit a uniform sampling. The potential discrepancy between the resulting connectivity and the original one is corrected at the end of the algorithm. We provide a proof-of-concept implementation, yielding very competitive results compared to previous works in terms of rate/distortion trade-off.     

基于逆3 细分的渐进网格生成算法研究

提出一种基于逆3 细分的渐进网格生成算法,用于解决图形的快速传输和显示问 题。算法的基本思路是：将细密网格通过边折叠操作得到简化网格,以细分极限点逼近原始网 格为准则进行网格调整,采用3 细分得到高密度网格,调整后进行逆3 细分,即逐层次删除 部分顶点,生成用于重构渐进网格模型的基网格,并记录每层删除顶点在采用本层表示时相对 于细分计算位置的几何调整量。3 细分过程中三角片数量增长速度较慢,采用逆3 细分利于 生成多层次的渐进网格,经实例验证,逆3 细分生成渐进网格的效果能满足快速、多分辨率显 示要求。