基于三维TIN的精细表面建模方法*

对现有三维不规则三角网（3DTIN）生成算法作了简要分类,回顾和评价了各类典型方法的优缺点和适用性,然后在此基础上提出了一种融合雕刻算法和生长算法优势的合成算法,给出了相应的数据结构。算法基于表面三角形任意一边的邻域结构,采用加权最小长度准则实现表面的快速生长。应用实例表明,算法可以重构具有任意拓扑的复杂表面,并且重构的三角网格表面与被采样的物体表面拓扑差别最小。     

On surface reconstruction: A priority driven approach

To reconstruct an object surface from a set of surface points, a fast, practical, and efficient priority driven algorithm is presented. The key idea of the method is to consider the shape changes of an object at the boundary of the mesh growing area and to create a priority queue to the advancing front of the mesh area according to the changes. The mesh growing process is then driven by the priority queue for efficient surface reconstruction. New and practical triangulation criteria are also developed to support the priority driven strategy and to construct a new triangle at each step of mesh growing in real time. The quality and correctness of the created triangles will be guaranteed by the triangulation criteria and topological operations. The algorithm can reconstruct an object surface from unorganized surface points in a fast and reliable manner. Moreover, it can successfully construct the surface of the objects with complex geometry or topology. The efficiency and robustness of the proposed algorithm is validated by extensive experiments.     

Implicit Surface-Based Geometric Fusion

This paper introduces a general purpose algorithm for reliable integration of sets of surface measurements into a single 3D model. The new algorithm constructs a single continuous implicit surface representation which is the zero-set of a scalar field function. An explicit object model is obtained using any implicit surface polygonization algorithm. Object models are reconstructed from both multiple view conventional 2.5D range images and hand-held sensor range data. To our knowledge this is the first geometric fusion algorithm capable of reconstructing 3D object models from noisy hand-held sensor range data.This approach has several important advantages over existing techniques. The implicit surface representation allows reconstruction of unknown objects of arbitrary topology and geometry. A continuous implicit surface representation enables reliable reconstruction of complex geometry. Correct integration of overlapping surface measurements in the presence of noise is achieved using geometric constraints based on measurement uncertainty. The use of measurement uncertainty ensures that the algorithm is robust to significant levels of measurement noise. Previous implicit surface-based approaches use discrete representations resulting in unreliable reconstruction for regions of high curvature or thin surface sections. Direct representation of the implicit surface boundary ensures correct reconstruction of arbitrary topology object surfaces. Fusion of overlapping measurements is performed using operations in 3D space only. This avoids the local 2D projection required for many previous methods which results in limitations on the object surface geometry that is reliably reconstructed. All previous geometric fusion algorithms developed for conventional range sensor data are based on the 2.5D image structure preventing their use for hand-held sensor data. Performance evaluation of the new integration algorithm against existing techniques demonstrates improved reconstruction of complex geometry.     

A Delaunay-based region-growing approach to surface reconstruction from unorganized points

This paper presents a Delaunay-based region-growing (DBRG) surface reconstruction algorithm that holds the advantages of both Delaunay-based and region-growing approaches. The proposed DBRG algorithm takes a set of unorganized sample points from the boundary surface of a three-dimensional object and produces an orientable manifold triangulated model with a correct geometry and topology that is faithful to the original object. Compared with the traditional Delaunay-based approach, the DBRG algorithm requires only one-pass Delaunay computation and needs no Voronoi information because it improves the non-trivial triangle extraction by using a region-growing technique. Compared with the traditional region-growing methods, the proposed DBRG algorithm makes the surface reconstruction more systematic and robust because it inherits the structural characteristics of the Delaunay triangulation, which nicely complements the absence of geometric information in a set of unorganized points. The proposed DBRG algorithm is capable of handling surfaces with complex topology, boundaries, and even non-uniform sample points. Experimental results show that it is highly efficient compared with other existing algorithms.     

A mesh reconstruction algorithm driven by an intrinsic property of a point cloud

This paper presents an algorithm for reconstructing a triangle mesh surface from a given point cloud. Starting with a seed triangle, the algorithm grows a partially reconstructed triangle mesh by selecting a new point based on an intrinsic property of the point cloud, namely, the sampling uniformity degree. The reconstructed mesh is essentially an approximate minimum-weight triangulation to the point cloud constrained to be on a two-dimensional manifold. Thus, the reconstructed surface has only small topological difference from the surface of the sampled object. Topological correct reconstruction can be guaranteed by adding a post-processing step.     

Three-dimensional surface reconstruction using meshing growing neural gas (MGNG)

The neural network method, a relatively new method in reverse engineering (RE), has the potential to reconstruct 3D models accurately and fast. A neural network (NN) is a set of interconnected neurons, in which each neuron is capable of making autonomous arithmetic and geometric calculations. Moreover, each neuron is affected by its surrounding neurons through the structure of the network. This work proposes a new approach that utilizes growing neural gas neural network (GNG NN) techniques to reconstruct a triangular manifold mesh. This method has the advantage of reconstructing the surface of an n-genus freeform object without a priori knowledge regarding the original object, its topology or its shape. The resulting mesh can be improved by extending the MGNG into an adaptive algorithm. The proposed method was also extended for micro-structure modeling. The feasibility of the proposed method is demonstrated on several examples of freeform objects with complex topologies.     

点云重构三角网格的生长型神经气算法

为克服点云噪声、不均匀分布和复杂拓扑结构对三角网格重构的限制,改进了生长型神经气重构算法.以样本在网格局部投影作为神经元插入判据,自适应调节网格增长速度,保持几何变换与拓扑变换的协调.利用非流形边检测机制删除冗余连接,保持网格的拓扑有效性.网络学习过程中动态更新三角片结构,且在孔洞修复阶段扩大近邻查找范围,连接近邻节点中的边界点,直到网格收敛,最终得到正确的欧拉示性数.算例表明,改进的算法对带噪声点云具有鲁棒性,可根据非均匀点云的分布自动调整网格密度,且能重构具有复杂拓扑结构的曲面.重构的三角网格对曲面逼近精度较高,网格出度均匀,三角形近似等边.     

基于STL文件的Laplacian网格优化算法

针对三角网格模型优化算法对模型几何细节描述不够精确的问题,提出一种基于Laplacian坐标的网格模型全局优化算法。模型几何细节描述方面,采用网格顶点Laplacian坐标。网拓扑结构不变的前提下,可精确描述网格曲面局部几何特性。顶点重新定位方面,采用在最小二乘意义下求解由权重控制的包含顶点位置,以及Laplacian坐标双重约束的线性系统最优解的方法。实验结果表明,该算法在优化提高模型三角面片质量的同时,可较好地保留原始模型的几何细节。     

特征驱动的曲面重建

提出了基于散乱空间点集进行曲面重建的新方法,从点集的空间位置信息中提取待建曲面的内蕴特征量——法向和曲率,利用点集的这些特征信息来确定拓扑重建的搜索空间,采用面片生长的方式重建曲面。该方法在快速获得正确拓扑连接的同时,直接生成了用较少的面片就能保持曲面特征的优化网格。     

Edgebreaker: connectivity compression for triangle meshes

Edgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (sometimes called connectivity or topology) of three-dimensional triangle meshes. Edgebreaker improves upon the storage required by previously reported schemes, most of which can guarantee only an O(t log(t)) storage cost for the incidence graph of a mesh of t triangles. Edgebreaker requires at most 2t bits for any mesh homeomorphic to a sphere and supports fully general meshes by using additional storage per handle and hole. For large meshes, entropy coding yields less than 1.5 bits per triangle. Edgebreaker's compression and decompression processes perform identical traversals of the mesh from one triangle to an adjacent one. At each stage, compression produces an op-code describing the topological relation between the current triangle and the boundary of the remaining part of the mesh. Decompression uses these op-codes to reconstruct the entire incidence graph. Because Edgebreaker's compression and decompression are independent of the vertex locations, they may be combined with a variety of vertex-compressing techniques that exploit topological information about the mesh to better estimate vertex locations. Edgebreaker may be used to compress the connectivity of an entire mesh bounding a 3D polyhedron or the connectivity of a triangulated surface patch whose boundary need not be encoded. The paper also offers a comparative survey of the rapidly growing field of geometric compression     

基于重新划分的三角形网格简化的一种改进算法

基于重新划分的三角形网格简化方法能自动生成多细节层次模型，它的基本思想是:根据三角形网格的局部几何和拓扑特征将一定数量的点分布到原网格上,生成一个中间网格,移去中间网格中的老顶点,并对产生的多边形区域进行局部三角化,最后形成以新点为顶点的三角形网格.本文在已有算法的基础上,提出了一种分布新点的算法,从而克服了原有方法的局限性.它利用三角形顶点的曲率和三角形的面积两个因素来反映网格在每个三角形处的特征.文中给出的一组实例说明了算法的有效性.     

几何数据压缩的一种新算法

本文提出一种几何数据压缩的新算法,其基本思想是在已知物体网格边界的条件下,首先寻找边界的凹点,然后建立网格结点的特殊树结构,即横切面树,并将横切面树中相邻节点内网格结点之间的关系表示为链表（三角形条带）,按契约数结构及链表（三角形条带）编码、存储帮传输网格结点的连接关系,这种算法不同于Gabriel Taubin算法,它具有对顶点坐标、属性坐标及三角形连接关系压缩无损等许多优点。     

二阶多面体网格中关键特征控制的表面重建技术

针对基于二阶多节点多面体网格的表面重建过程中存在的准确拓扑及绘制、传输代价等问题,提出了一种基于关键特征控制的表面重建技术.研究并分析了二阶多节点多面体单元等参插值函数的性质特征,在网格单元棱边插值计算曲面轮廓点,在网格表面及体内提取曲面的几何特征关键点;根据3类插值关键点间的逻辑关系制定了令拓扑准确唯一的面片三角化规则及修复策略,设计了基于关键点的三角面片压缩索引结构.实验结果表明,该方法可准确计算并描述基于二阶多节点多面体网格单元的曲面几何拓扑结构,反映网格单元内部面片的真实凹凸性质,克服了拓扑二义性,具备对不同精度要求的适应性,并有效降低了绘制与传输代价.     

Mean Curvature Skeletons

Inspired by recent developments in contraction‐based curve skeleton extraction, we formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take advantage of its area‐minimizing characteristic to drive the curvature flow towards the extreme so as to collapse the input mesh geometry and obtain a skeletal structure. By analyzing the differential characteristics of the flow, we reveal that MCF locally increases shape anisotropy. This justifies the use of curvature motion for skeleton computation, and leads to the generation of what we call “mean curvature skeletons”. To obtain a stable and efficient discretization, we regularize the surface mesh by performing local remeshing via edge splits and collapses. Simplifying mesh connectivity throughout the motion leads to more efficient computation and avoids numerical instability arising from degeneracies in the triangulation. In addition, the detection of collapsed geometry is facilitated by working with simplified mesh connectivity and monitoring potential non‐manifold edge collapses. With topology simplified throughout the flow, minimal post‐processing is required to convert the collapsed geometry to a curve. Formulating skeletonization via MCF allows us to incorporate external energy terms easily, resulting in a constrained flow. We define one such energy term using the Voronoi medial skeleton and obtain a medially centred curve skeleton. We call the intermediate results of our skeletonization motion meso‐skeletons; these consist of a mixture of curves and surface sheets as appropriate to the local 3D geometry they capture.     

一种基于投影的散乱数据表面增量重建算法

针对3维散乱数据场提出了一种表面重建算法.根据空间曲面的局平特性和平面三角化的基本原则,在参考点的切平面上对邻域点按角度排序,应用可见性准则删除不可见点后,相邻邻域点和参考点形成三角网格.将平面上的网格关系对应到空间,以增量方式重建反映散乱数据场拓扑关系的空间曲面.设定角度阈值优化网格,判断空间曲面的边界和孔洞.对多个数据场进行重建并对结果进行分析.对多个数据场进行重建并对结果进行分析表明,算法具有原理简单,重建速度快,重建效果好的特点.     

Mesh repair with user-friendly topology control

Limitations of current 3D acquisition technology often lead to polygonal meshes exhibiting a number of geometrical and topological defects which prevent them from widespread use. In this paper we present a new method for model repair which takes as input an arbitrary polygonal mesh and outputs a valid 2-manifold triangle mesh. Unlike previous work, our method allows users to quickly identify areas with potential topological errors and to choose how to fix them in a user-friendly manner. Key steps of our algorithm include the conversion of the input model into a set of voxels, the use of morphological operators to allow the user to modify the topology of the discrete model, and the conversion of the corrected voxel set back into a 2-manifold triangle mesh. Our experiments demonstrate that the proposed algorithm is suitable for repairing meshes of a large class of shapes.     

以复形为基础的非流形造型与基于物理的造型相结合的物体表示

提出一个新的表示物体的框架。通过非流形造型与基于物理的造型相结合，从拓扑结构和几何信息两个方面扩大了模型的表示范围。以代数拓扑中的复形为基础的非流形造型的作用是生成物体的拓扑框架，既可以表示ＣＡＤ的物体，更适合表示具有复杂拓扑结构的自然物体。基于物理的造型的作用是在拓扑框架上生成最终的几何信息。二者的结合提供了一种新的几何造型手段。     

用内法向量与二次误差度量修补三角网格孔洞

为了高效地修复含孔洞的三角网格模型,提出基于内法向量与二次误差度量(QEM)的孔洞修补算法.在识别孔洞边界之后,计算边界点的凹凸性与对应夹角角度,并利用最小角-曲率原则寻找最优修补点;根据三角形生成原则以及内法向计算方法生成新的三角形完成粗修补;最后利用二次型误差滤波函数对粗修补的网格进行优化处理.在VisualStudio2013环境下,对不同种类的含孔洞模型,利用提出算法以及孔洞修补经典算法进行实验,结果表明,文中算法修补的网格质量优于对比算法.     

离散曲率约束的三角网格模型拓扑分割算法

针对三角形网格模型简化中保持细节特征的要求,提出了依据离散曲率划分三角网格顶点的特性,并结合区域增长法自适应地确定拓扑分支的优化算法.每个顶点根据其相邻面片顶点的曲率值划分属性区域,并在区域生长过程中重复选择K-ring碟形区域中具有相似属性值的顶点作为种子.为了有效地探索凸凹形状区域,以曲率极值点作为初始点,提出了有效的区域增长及合并的策略,突出了模型的局部特征和拓扑结构.最后通过一系列实验验证了该算法的快捷性.