三角网格模型的补洞算法研究

提出了一种三角网格模型的空间孔洞修补算法.首先根据网格中的点、边和三角形之间的关系提取孔洞边界,然后根据孔洞区域的夹角的顺序在空间中依次填补三角形直至修补完全,接着对新增加的高度弯曲的三角形进行细分,最后对修补后的孔洞网格进行几何形态调整,光顺化整个孔洞曲面.实验结果证明,该算法简单、有效,孔洞修补效果好.     

三维模型孔洞修补方法的研究

针对三维模型中带有各种原因造成的孔洞, 为后续的模型分析操作带来困难, 提出了一种基于曲率特征的三维模型孔洞修补方法。其基本思想是利用波前法对孔洞进行快速填充获得初始的修补网格, 再运用网格优化的技术依据孔洞边界点的曲率特征对初始网格进行调整。首先根据邻接三角形中边界边的性质识别出孔洞的边界, 然后使用波前法和三角形顶点的夹角关系完成孔洞的初始填充, 接着结合曲率标准对孔洞网格进行细化, 最后对修补孔洞的网格顶点进行几何形态的调整, 使其与周围网格自然过渡。实验表明该算法简单、稳定, 可以完成不同类型的孔洞修补。     

基于两步的网格平滑

在三角网格的生成过程中,不可避免地会出现噪声,如何有效地消除这些噪声已经成为当前计算机图形学领域的一个重要课题,提出了一个简单的,能有效去除噪声,同时能很好的保持网格尖边特征的算法.该算法通过两步来实现,第一步对三角网格的三角面面法矢量进行平滑,第二步依据面法矢量调整新的顶点坐标.此算法在伪三角的帮助下,能很好保持曲面的几何特征,防止曲面收缩.实验结果说明了实验的有效性.     

Obtuse triangle suppression in anisotropic meshes

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy.     

Surface interpolation of meshes by geometric subdivision

Subdivision surfaces are generated by repeated approximation or interpolation from initial control meshes. In this paper, two new non-linear subdivision schemes, face based subdivision scheme and normal based subdivision scheme, are introduced for surface interpolation of triangular meshes. With a given coarse mesh more and more details will be added to the surface when the triangles have been split and refined. Because every intermediate mesh is a piecewise linear approximation to the final surface, the first type of subdivision scheme computes each new vertex as the solution to a least square fitting problem of selected old vertices and their neighboring triangles. Consequently, sharp features as well as smooth regions are generated automatically. For the second type of subdivision, the displacement for every new vertex is computed as a combination of normals at old vertices. By computing the vertex normals adaptively, the limit surface is G¹ smooth. The fairness of the interpolating surface can be improved further by using the neighboring faces. Because the new vertices by either of these two schemes depend on the local geometry, but not the vertex valences, the interpolating surface inherits the shape of the initial control mesh more fairly and naturally. Several examples are also presented to show the efficiency of the new algorithms.     

曲率约束的隐式曲面三角网格化

提出一种有效的隐式曲面三角网格化算法。从隐式曲面上的一个种子点开始,生成网格的边界作为扩张多边形,且该多边形最小角对应的顶点为扩张点,计算从扩张点处欲生成的三角网格,为了防止新生成的三角网格和已经存在的三角网格重叠,要进行冲突检测。在隐式曲面三角网格化的过程中,扩张多边形是不断变化的,需要重复上述步骤,直至没有扩张多边形时结束。该算法分别应用于解析隐式曲面和变分隐式曲面的三角网格化。实验结果表明,该算法不需要重新网格化的步骤,生成的三角网格具有较高的质量,且三角网格随曲率适应性变化,因此说明了该算法的有效性。     

基于近平面合并的三角网格简化算法

提出一种基于近平面合并的三角网格简化算法,针对三维重建MarchingCubes算法中产生的大量三角片进行简化。首先依据近平面判断条件将近似共面的三角形合并成一个大的多边形,然后按相应的准则将其重新进行三角化得到更少的三角形面片,以达到简化的目的。该算法在最大化的保留图像细节的前提下,精简了三角片的数目,提高了重建后图像绘制和传输的速率,节省了存储空间和处理时间。     

High-quality 2D mesh generation without obtuse and small angles

In this paper, we present an efficient method to eliminate the obtuse triangles for high quality 2D mesh generation. Given an initialization (e.g., from Centroidal Voronoi Tessellation—CVT), a limited number of point insertions and removals are performed to eliminate obtuse or small angle triangles. A mesh smoothing and optimization step is then applied. These steps are repeated till a desired good quality mesh is reached. We tested our algorithm on various 2D polygonal domains and verified that our algorithm always converges after inserting a few number of new points, and generates high quality triangulation with no obtuse triangles.     

基于控制点误差控制的网格简化算法

提出了一种基于控制点误差控制的网格简化算法，以初始网格三角形的中心点作为第一类控制点，以特征边的顶点作为第二类控制点，控制点与受控三角形之间的距离作为简化误差。根据设定的三角形权重，按照顺序进行三角形折叠操作，简化操作后必须满足控制点到受控三角形的距离小于阈值。     

Efficient mesh denoising via robust normal filtering and alternate vertex updating

The most challenging problem in mesh denoising is to distinguish features from noise. Based on the robust guided normal estimation and alternate vertex updating strategy, we investigate a new feature-preserving mesh denoising method. To accurately capture local structures around features, we propose a corner-aware neighborhood (CAN) scheme. By combining both overall normal distribution of all faces in a CAN and individual normal influence of the interested face, we give a new consistency measuring method, which greatly improves the reliability of the estimated guided normals. As the noise level lowers, we take as guidance the previous filtered normals, which coincides with the emerging rolling guidance idea. In the vertex updating process, we classify vertices according to filtered normals at each iteration and reposition vertices of distinct types alternately with individual regularization constraints. Experiments on a variety of synthetic and real data indicate that our method adapts to various noise, both Gaussian and impulsive, no matter in the normal direction or in a random direction, with few triangles flipped.     

基于三角形折叠的网格简化算法

在计算机图形学中，物体常常用三角形网格模型来描述。本文提出了一种新的基于三角形折叠的网格简化算法。该网格简化算法不仅能减少模型中的三角形数目而且能保持模型拓扑结构。算法给出了一种基于点到平面距离的有效的误差控制方法，并能在用户指定的误差范围内通过使原始网格中的三角形折叠达到大量简化的目的。该算法实现简单并且速度快。另外为了有效地支持多分辨率模型的表示以及相邻层次模型间的连续过渡，本文还给出了一种基     

基于径向基函数的三角网格曲面孔洞修补算法

提出一种对三角网格曲面中孔洞的修补算法,在对孔洞多边形进行填补后,使用径向基函数建立孔洞曲面的隐式方程,然后把新增加的三角片顶点映射到曲面上．由于在修补时不仅考虑了对孔洞多边形的三角划分问题,还考虑了孔洞周围的几何信息,使得修补后的孔洞曲面与原始曲面光滑地融为一体,尤其对曲率变化较剧烈部位处的孔洞取得了理想的修补效果．     

一种适合VRML应用的三角网格简化算法

交互虚拟环境中，VRML作为三维场景描述语言得到广泛应用，场景中的物体常常用三角形网格模型来描述，本文提出了一种适合VRML应用的网格简化算法，该算法不仅可以快速减少模型中的画片数目而且能保持模型良好的视觉效果，算法中给出了一种有效的误差控制方法，能在用户指定的误差范围内通过使原始网格中的边折叠达到大量简化的目的，该算法实现简单且速度快，另外能够有效地支持细节层次模型的表示，最后给出实例证明了该算法的有效性。     

基于体积误差的三角形收缩网格简化算法

本文提出了一种基于体积误差的三角形收缩网格简化算法。根据体积误差方程和指定的体积误差门限,通过计算体积误差的最小值把对应的三角形收缩到一点,从而简化了表示物体模型的三角形网格。实验结果表明,这种算法简化效果好、效率高,误差可以控制。     

Approximating isosurfaces by guaranteed-quality triangular meshes

We describe a new method for approximating an implicit surface F by a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The main advantage is improved mesh quality which is guaranteed for smooth surfaces. The GradNormal algorithm generates a triangular mesh that gives a piecewise-differentiable approximation of F, with angles between 35.2 and 101.5 degrees. As the mesh size approaches 0, the mesh converges to F through surfaces that are isotopic to F.     

一种随机采样的特征保持的网格简化算法

提出了一种局部几何特征驱动的随机采样的网格简化算法。该算法首先计算模型中每个三角形的局部几何特征值,根据定义的概率分布函数随机确定每个三角形被选择的概率。然后对选择出的三角形进行三角形折叠,根据折叠前后网格体积变化最小这一准则来确定新生成的顶点的位置。实验证明该算法不仅能使简化前后的模型的体积变化较小,还能有效地保持模型的细节特征。     

A two-dimensional paving mesh generator for triangles with controllable aspect ratio and quadrilaterals with high quality

Certain classes of problems result in solution fields of which the characteristic length scales vary with the orientation. Often the orientation of these length scales is related to the orientation of the boundaries. Such solution fields can be captured by the finite element method, using a mesh that is refined in the direction of the short length scales and coarse in the other directions. These meshes contain elements with high aspect ratios in a predefined pattern.The mesh generator presented here can render triangles with high aspect ratios through a paving algorithm. The paving algorithm that is employed applies both triangles and quadrilaterals, combining the advantages of both to render a qualitatively good, oriented triangular mesh, with a concentration of elements in the direction where the internal length scales of the solution field are the shortest.The mesh generator produces triangles with one (almost) orthogonal corner. When low aspect ratio triangles are generated, these are well suited for conversion to quadrilateral elements. Test results indicate that quadrilateral meshes converted from the mesh generator introduced here have a considerably better quality than those converted from several other triangular mesh generators.     

散乱点云的三角网格重构

基于增量扩散法的思想,提出并实现了一个散乱点云的三角网格重构算法,算法首先利用体素网格的散列表对散乱点进行组织,然后在确定了初始种子三角形的基础上,基于活动边扩展规则构造新的三角形,使网格不断向周围扩展直到活动边表空为止,最后算法合并棱边并计算每个三角形的顶点法矢,最终构造出散乱点云的三角网格。     

A piecewise hole filling algorithm in reverse engineering

While scanning a complex part in reverse engineering, it is not possible to acquire all part of the scanned surface. Data are inevitably missing due to the complexity of the scanned part or imperfect scanning process. Missing scanned data cause holes in the created triangular mesh, so that a hole-free mesh model is prerequisite for fitting watertight surfaces. Although a number of hole filling algorithms have been investigated, they enable to fill holes only on the smooth regions of a model. They are not always robust in the regions of high curvature. This paper proposes a novel methodology that can automatically fill complex polygonal holes with a piecewise manner. It incrementally splits a complex hole into several simple holes with respect to the 3D shape of the hole boundary, and then it consecutively fills each divided simple hole with planar triangulation method until the entire complex hole is firmly closed. Finally smoothing and subdivision techniques are applied for enhancing the hole triangles. The newly created vertices and triangles are added to their respective lists and the topology information is updated. The method has proven to be robust and effective from the result of test with a variety of complex holes. Examples are given and discussed to validate the methodology.     

ARTMe: a new array-based algorithm for Adaptive Refinement of Triangle Meshes

Engineering with Computers - This work presents a new efficient array-based algorithm for adaptive mesh refinement capable of interactively generating millions of triangles. The new refinement...