一种基于三维Delaunay三角化的曲面重建算法

提出一种基于三维Delaunay三角化的区域增长式曲面重建方法。该方法以空间点云的Delaunay三角化为基础,结合局部区域增长的曲面构造,较以往方法具有人为参与更少、适用范围更广的优点。算法采用增量式插入点的方式构建空间Delaunay划分,采用广度优先算法,以外接圆最小为准则从Delaunay三角化得到的四面体中抽取出合适的三角片构成曲面。该算法的设计无须计算原始点集的法矢,且孔洞系数对重建的结果影响很小,重建出的三角网格面更符合原始曲面的几何特征。无论待建曲面是否是封闭曲面,本算法均可获得较好的重建效果。     

实现3D离散点优化三角划分的三维算法

本文系统研究了３Ｄ离散数据的直接三角划分，并解决了与多值曲面相对应离散数据的分片三角划分问题。实现这一算法的关键是将这些与多值曲面相对应的离散数据按有关的特征线分解，慢之转化成较简单的问题分别进行处理。目前，这种分片三角划分算法已在Ｂｅｚｉｅｒ三角曲面插值中取得了良好的效果。     

多连通曲面离散点集的3D三角划分算法研究

在对非封闭曲面、简单封闭曲面和多连通封闭曲面的特点进行分析之后,提出了一种多连通封闭曲面离散点集的3D三角划分算法.该算法无须对离散点集所对应的自由曲面进行分片,直接在3D空间根据曲面的形态变化向前逐层推进生成三角网格.算法同时还适用于非封闭曲面和简单封闭曲面两种情形.实验结果表明,该算法的划分效果优良,能够满足曲面重构的需要.     

由深度数据重建三维物体的一种方法

讨论由深度数据重建三维物体的一种新方法.其基本思想是根据由基于物体旋转的主动 式三角法三维信息获取系统所获取的物体深度数据作为该物体的型值点.再根据型值点进行 网格划分,以便形成满足一定约束条件的空间拓扑网格.最后使用有理Bezier三角曲面片与 矩形曲面片相结合的方法进行曲面拟合与逼近.     

三维重构中轮廓线间的连接和光滑问题的处理

在使用面绘制算法重构三维实体模型时,由于原始数据稀疏,需要通过一定的方法对填充在相邻轮廓线间的三角形或多边形进行拟和,以达到光滑的效果。本文先按照最小内角最大准则进行Delaunay三角剖分,当可选三角形的最小内角相等时再运用最短路径法在相邻轮廓线间构造三角形,然后再在三角格网上构造Bezier三角曲面,不仅使构造出来的格网具有较好形状,又提高了表面的光滑程度和重构的精度。     

散乱数据点集的三角划分算法研究

在对当前的三角网格划分方法进行比较分析后,提出了一种散乱数据点集的3D三角网格划分算法,该算法不需如同二维划分方法一样要对散乱点集对应的自由曲面分片投影,并可自然处理含有凹边界及孔域的曲面数据点集,利用网格扩展、边界环分裂和边界环封闭,根据曲面的变化逐层推进生成三角网格,使算法能方便地处理非封闭曲面、空间剪裁曲面、封闭曲面、空间多连通曲面等各种曲面的散乱数据。     

Data structures for encoding triangulated irregular networks

Triangulated Irregular Networks are the most common form of digital surface model. They are based on a decomposition of the surface into a set of non-overlapping triangular patches. In the paper, we consider the problem of the internal representation of triangular subdivisions. We describe four different data structures, which are especially well-suited to represent triangular grids. Algorithms for solving three basic problems on triangulated irregular networks, namely the point-in-triangulation, the vertex-neighbor and the edge-neighbor problems, are described, and their time complexity is evaluated.     

基于八叉树和混合搜索树的地质曲面快速求交方法

为处理地质界面之间的空间相交关系,提出一种新的针对三角地质曲面的快速求交方法。该方法融合优化八叉树法和OBB搜索树方法,可以更快速准确地剔除远离交线的其他三角形。求交剩余的三角形得到交线,应用三角网局部重构和网格优化算法修正交线附近的三角网,最终分割交线两侧的地质曲面,完成2个地质曲面的离散化求交过程。与AABB、OBB和空间分解法相比,该方法在大数据量三角曲面求交中效率优势明显,可以快速准确处理地质模型构建和分析中的曲面求交问题,为三维地质模型自动化构建的实现提供有效支撑。     

Hierarchical grid conversion

Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, it is desired to switch between regular grids to take advantages of these grids. Based on a 2D domain obtained from the connectivity information of a mesh, we can define simple conversions to switch between regular grids. In this paper, we introduce a general framework that can be used to convert a given grid to another and we discuss the properties of these refinements such as their transformations. This framework is hierarchical meaning that it provides conversions between meshes at different level of refinement. To describe the use of this framework, we define new regular and near-regular refinements with good properties such as small factors. We also describe how grid conversion enables us to use patch-based data structures for hexagonal cells and near-regular refinements. To do so, meshes are converted to a set of quadrilateral patches that can be stored in simple structures. Near-regular refinements are also supported by defining two sets of neighborhood vectors that connect a vertex to its neighbors and are useful to address connectivity queries.     

自适应T样条曲面重建

为了进行快速高精度的曲面重建,提出了一种新的基于T样条的曲面自动重建算法。由于T样条控制网格具有特殊性质,因此在使用T样条进行曲面重建时,一个关键的问题是如何构造好一个T网格。该新算法在进行曲面重建时,用三角网格的参数化方法,先将数据点同胚映射到平面,然后再利用平面四叉树细分的方法将无结构散乱数据自动生成合理有效的T网格,最后将曲面重构模型转化为最优化问题,并由最小二乘法求解,同时在误差较大的区域辅以T样条的局部修正,以使重建曲面与原网格面的最大误差小于指定的误差值。由于该新的曲面重建方法是一个基于细节的重建方法,因此采样点密集区域所插入的T网格点也就相应地增多,这样既抓住了网格曲面的特征,又能很好地减少过多的T网格控制顶点,这就提高了算法效率。另外,该新算法还具有高效、易操作、能适应复杂曲面重建、曲面自动生成且满足相应精度要求等优点。重构结果显示,该新的曲面重建算法不仅重构应用范围广,且重构精度高。     

任意三角形网格的基于二元四次箱样条分片C1曲面

提出一种以任意三角剖分为控制网格的二元箱样条曲面算法.二元三方向剖分是方向最少的三角剖分,建立在其上的二元三向四次箱样条在CAGD等领域有着广泛的应用.其规范的箱样条曲面计算仅适用于控制点的价数均为6的网格.从规范的算法出发,提出了一种任意价数控制网格的曲面计算算法,并对算法的连续性等进行了详细的分析.生成的曲面具有保凸性,且是分片C1连续的.该算法可进行3D离散点全局或局部插值,并可应用于3D曲面重构等领域.     

任意三角形网格的基于二元四次箱样条分片C1曲面

提出一种以任意三角剖分为控制网格的二元箱样条曲面算法.二元三方向剖分是方向最少的三角剖分,建立在其上的二元三向四次箱样条在CAGD等领域有着广泛的应用.其规范的箱样条曲面计算仅适用于控制点的价数均为6的网格.从规范的算法出发,提出了一种任意价数控制网格的曲面计算算法,并对算法的连续性等进行了详细的分析.生成的曲面具有保凸性,且是分片C¹连续的.该算法可进行3D离散点全局或局部插值,并可应用于3D曲面重构等领域.     

Minimal roughness property of the Delaunay triangulation

A set of scattered data in the plane consists of function values measured on a set of data points in R². A surface model of this set may be obtained by triangulating the set of data points and constructing the Piecewise Linear Interpolating Surface (PLIS) to the given function values. The PLIS is combined of planar triangular facets with vertices at the data points. The roughness measure of a PLIS is the L² norm squared of the gradient of the piecewise linear surface, integrated over the triangulated region and obviously depends on the specific triangulation. In this paper we prove that the Delaunay triangulation of the data points minimizes the roughness measure of a PLIS, for any fixed set of function values. This Theorem connects for the first time, as far as we know, the geometry of the Delaunay triangulation with the properties of the PLIS defined over it.     

一种面向三维点集的快速表面重构算法

在对目前比较流行的空间三角化算法进行对比研究的基础上 ,对 Hugues Hoppe提出的算法进行了改进 ,即借鉴 Marching Cubes算法的基本思想 ,首先通过自动选取适当的参数 ,用包围盒方法将三维散乱点划分为数据区域 ;然后求取点的切平面及法向 ,同时采用广度优先算法遍历数据点来调整法向和快速地求取 Marching Cubes的等势函数 ;最后用基于查表法的 Marching Cubes来输出三角面片 ,即得到表面模型 .实验结果表明 ,改进后的算法效率有较大的提高 .新算法不仅适用于表面三维散乱点数据 ,也可以对体数据进行重构 ,具有一定的通用性 .     

An adaptive method for smooth surface approximation to scattered 3D points

The construction of a surface from arbitrarily scattered data is an important problem in many applications. When there are a large number of data points, the surface representations generated by interpolation methods may be inefficient in both storage and computational requirements. This paper describes an adaptive method for smooth surface approximation from scattered 3D points. The approximating surface is represented by a piecewise cubic triangular Bézier surface possessing C¹ continuity. The method begins with a rough surface interpolating only boundary points and, in the successive steps, refines it by adding the maximum error point at a time among the remaining internal points until the desired approximation accuracy is reached. Our method is simple in concept and efficient in computational time, yet realizes efficient data reduction. Some experimental results are given to show that surface representations constructed by our method are compact and faithful to the original data points.     

A hierarchical structure for surface approximation

Hierarchical triangulation is a method for point selection and surface representation where the surface is approximated at successively finer levels of detail by triangular patches whose projections in the horizontal plane are nested. A tree data structure for this representation can be constructed in O(n²) worst case and O(n log n) average case time, where n is the number of data points considered. Efficient algorithms for approximation of the elevation of an arbitrary point, contour extraction, and conversion of the hierarchical structure into an ordinary triangulated irregular network, are demonstrated. The convergence and the optimality of the approximation and the relationship of the hierarchical triangulation to a structured graph representation are examined.     

Approximating digital 3D shapes by rational Gaussian surfaces

A method for approximating spherical topology digital shapes by rational Gaussian (RaG) surfaces is presented. Points in a shape are parametrized by approximating the shape with a triangular mesh, determining parameter coordinates at mesh vertices, and finding parameter coordinates at shape points from interpolation of parameter coordinates at mesh vertices. Knowing the locations and parameter coordinates of the shape points, the control points of a RaG surface are determined to approximate the shape with a required accuracy. The process starts from a small set of control points and gradually increases the control points until the error between the surface and the digital shape reduces to a required tolerance. Both triangulation and surface approximation proceed from coarse to fine. Therefore, the method is particularly suitable for multiresolution creation and transmission of digital shapes over the Internet. Application of the proposed method in editing of 3D shapes is demonstrated.     

Multiresolution model based extraction of product feature lines in reverse engineering

In this paper, multiresolution models are employed in the context of reverse engineering for feature line extraction. Starting with a proper triangulation of the cloud point data as a priori, our feature line extraction algorithm has three steps: (1) establishing a Gauss normal sphere and creating multiresolution models for the Gauss sphere based on different levels of subdivisions for the sphere regions; (2) mapping the unit normal vectors of triangular faces in the multiresolution Gauss sphere and merging those connected triangular faces whose unit normal vectors fallen on the same Gauss sphere region with a given resolution to form super-faces (the collection of triangular facets with similar normal); and (3) extracting the boundaries from the super-faces and generating the feature lines from the extracted boundaries. We then use these feature lines as a base for tracing boundary curves for B-spline surface construction. Since feature lines maintain the characteristics of the original product models, in this way, we have a good chance to reconstruct B-spline surfaces with high quality. Examples are given in the paper to show the feature line extraction, the influence of the feature lines extracted under different resolutions, and the final reconstructed B-spline surfaces based on these feature lines.     

基于均匀网格的Delaunay三角网算法在随机聚合网屏中的应用

Delaunay三角网一直是一个重要而有意义的研究课题，并具有极其广泛的用途。经过20多年来的研究，它的生成算法已趋于成熟。为了满足印刷、印染系统中随机聚合网屏生成的实时性需要，将一种将的算法引处到FM网屏技术中，并首先简要介绍了Delaunay三角网的牧场考及生成算法的分类；然后主要介绍了一种基于均匀网格的Delaunay三角网生成算法在随机聚合网屏中的应用；最后给出了算法的正确性证明。经测试，该算法的运算速度相当快，具有接近于线性的时间复杂性，能够满足排版印刷、印染系统中随机聚合网屏生成的需要。     

复合三角Bézier曲面求交和裁剪的实现

该文利用三角Bézier曲面片的可分割性,解决了迭代收敛、初始交点计算等问题;通过近曲面点、边界点跨越等过程,实现了由一个初始交点将跨越许多曲面片的整条交线跟踪出来的设想.将各交点作为型值点插入曲面中,对三角网格进行三角再划分,以交线为界进行三角网格和型值点的分离,最后重新生成两张复合曲面,实现了裁剪的目的.测试结果显示,此方法简单、可靠,能够满足曲面造型的要求.