A comprehensive process of reverse engineering from 3D meshes to CAD models

In an industrial context, most manufactured objects are designed using CAD (Computer-Aided Design) software. For visualization, data exchange or manufacturing applications, the geometric model has to be discretized into a 3D mesh composed of a finite number of vertices and edges. However, the initial model may sometimes be lost or unavailable. In other cases, the 3D discrete representation may be modified, e.g. after numerical simulation, and no longer corresponds to the initial model. A retro-engineering method is then required to reconstruct a 3D continuous representation from the discrete one.In this paper, we present an automatic and comprehensive retro-engineering process dedicated mainly to 3D meshes obtained initially by mechanical object discretization. First, several improvements in automatic detection of geometric primitives from a 3D mesh are presented. Then a new formalism is introduced to define the topology of the object and compute the intersections between primitives. The proposed method is validated on 3D industrial meshes.     

3D网格的分层多描述编码方法

结合分层编码与多描述编码的优势,提出三维网格分层多描述编码（LMDC）方法：先对3D网格进行几何分解,得到一个粗糙网格和细化网格所需的连通性信息,采用分层编码思想,粗糙网格作为基本层,而将细化信息作为增强层。同时采用基于顶点分裂树的多描述编码方法对基本层加以保护,保证基本层在差错信道中的有效传输。采用分层多描述编码对3D模型进行编码的方法,非常适合于带宽受限和多路径传输的异构网络。实验证明,该方法能获得较高的压缩率,并在有丢包的情况下能有效地保护并恢复出可接受的基本层网格。     

A framework for 3D model reconstruction in reverse engineering

We present a framework for 3D model reconstruction, which has potential applications to a spectrum of engineering problems with impacts on rapid design and prototyping, shape analysis, and virtual reality. The framework, composed of four main components, provides a systematic solution to reconstruct geometric model from the surface mesh of an existing object. First, the input mesh is pre-processed to filter out noise. Second, the mesh is partitioned into segments to obtain individual geometric feature patches. Then, two integrated solutions, namely solid feature based strategy and surface feature based strategy, are exploited to reconstruct primitive features from the segmented feature patches. Finally, the modeling operations, such as solid boolean and surface trimming operations, are performed to “assemble” the primitive features into the final model. The concepts of “feature”, “constraint” and “modeling history” are introduced into the entire reconstruction process so that the design intents are retrieved and exhibited in the final model with geometrical accuracy, topological consistency and flexible editability. A variety of industrial parts have been tested to illustrate the effectiveness and robustness of our framework.     

An algorithm for filling complex holes in reverse engineering

The existence of holes in meshes makes it difficult for mesh operations, especially when comes to model rebuilding, rapid prototyping and finite element analysis. Existing hole-filling algorithms are capable of filling holes on small and smooth regions of a model. For large holes with complex boundaries or in curved region, they may not result in satisfactory results. This paper proposes an algorithm which first split the holes into flatter ones and then split the complex holes based the concept of edge expansion. It incrementally splits a complex hole into simple ones by respecting the 3D shape of its boundary and the neighboring meshes, and then fills each resulting simple hole with planar triangulation. The proposed algorithm works well for a variety of complex holes and can better preserve the detailed features of the original mesh.     

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.     

Motorcycle graph enumeration from quadrilateral meshes for reverse engineering

Recently proposed quad-meshing techniques allow the generation of high-quality semi-regular quadrilateral meshes. This paper outlines the generation of quadrilateral segments using such meshes. Quadrilateral segments are advantageous in reverse engineering because they do not require surface trimming or surface parameterization. The motorcycle graph algorithm of Eppstein et al. produces the motorcycle graph of a given quadrilateral mesh consisting of quadrilateral segments. These graphs are preferable to base complexes, because the mesh can be represented with a smaller number of segments, as T-joints (where the intersection of two neighboring segments does not involve the whole edge or the vertex) are allowed in quadrilateral segmentation.The proposed approach in this study enumerates all motorcycle graphs of a given quadrilateral mesh and optimum graph for reverse engineering is then selected. Due to the high computational cost of enumerating all these graphs, the mesh is cut into several sub-meshes whose motorcycle graphs are enumerated separately. The optimum graph is then selected based on a cost function that produces low values for graphs whose edges trace a large number of highly curved regions in the model. By applying several successive enumeration steps for each sub-mesh, a motorcycle graph for the given mesh is found. We also outline a method for the extraction of feature curves (sets of highly curved edges) and their integration into the proposed algorithm. Quadrilateral segments generated using the proposed techniques are validated by B-spline surfaces.     

Adaptive fairing of digitized point data with discrete curvature

An algorithm for fairing two-dimensional (2D) shape formed by digitised data points is described. The application aims to derive a fair curve from a set of dense and error-filled data points digitised from a complex surface, such that the basic shape information recorded in the original point data is relatively unaffected. The algorithm is an adaptive process in which each cycle consists of several steps. Given a 2D point set, the bad points are identified by analysing the property of their discrete curvatures (D-curvatures) and first-order difference of D-curvatures, in two consecutive fairing stages. The point set is then segmented into single bad point (SBP) segments and multiple bad point (MBP) segments. For each MBP segment, a specially designed energy function is used to identify the bad point to be modified in the current cycle. Each segment is then faired by directly adjusting the geometric position of the worst point. The amount of adjustment in each cycle is kept less than a given shape tolerance. This algorithm is particularly effective in terms of shape preservation when dealing with MBP segments. Case studies are presented that illustrate the efficacy of the developed technique.     

Parallel decoupled terminal-edge bisection method for 3D mesh generation

We present a practical and stable algorithm for the parallel refinement of tetrahedral meshes. The algorithm is based on the refinement of terminal-edges and associated terminal stars. A terminal-edge is a special edge in the mesh which is the longest edge of every element that shares such an edge, while the elements that share a terminal-edge form a terminal star. We prove that the algorithm is inherently decoupled and thus scalable. Our experimental data show that we have a stable implementation able to deal with hundreds of millions of tetrahedra and whose speed is in between one and two order of magnitude higher from the method and implementation we presented (Rivara et al., Proceedings 13th international meshing roundtable, 2004).Maria-Cecilia Rivara and Carlo Calderon's work was partially supported by Fondecyt 1040713.Andriy Fedorov’s work is supported in part by ITR #ACI-0085969, and NGS #ANI-0203974.Nikos Chrisochoides’s work is supported in part by NSF Career Award #CCR-0049086, ITR #ACI-0085969, NGS #ANI-0203974, and ITR #CNS-0312980.     

新颖的网格模型压缩算法——网格切片

针对三维(3D)网格模型的存储与网络传输问题,提出一种新颖的三维模型压缩算法。该算法基于对网格模型的切片处理,主要由以下三个步骤组成:切片顶点的计算、切片边界的均匀采样以及对切片所得图像的编码。对于一个给定的三维模型,首先,计算模型的包围盒;然后,沿包围盒长度最长的方向进行切片;同时计算切片与网格模型表面每条边的交点,构成一个多边形,这个多边形即为切片的边界;其次,对切片边界进行均匀的重采样,使每层切片具有相同的顶点数;最后,把每层的顶点坐标转化为极坐标形式,这样,所有层顶点的ρ-坐标以及θ-坐标能分别构成一张图像,原始的三维模型即能由这两张图像表示。这种表示方法具有以下两个明显的优势:第一,降低了数据的维度,有效减少了数据量;第二,具有极大的数据相关性,进一步减少了数据的熵。基于这两个优势,该算法对图像数据进行差值编码以及算术编码,最后得到压缩后的文件。与增量参数细化(IPR)方法相比,在解码模型同等质量的前提下,所提算法的编码效率提高了23%。实验结果表明,所提算法在模型存储和传输应用中能取得很好的压缩效率,有效减少了数据量。     

三维网格模型的快速拓扑重建算法

为了提高重建三维网格模型拓扑的速度,选择半边结构作为表示实体模型拓扑关系的结构模型,设计了新的用于加快顶点合并的索引方法。在顶点合并时直接定位到欲查找的顶点位置上,无须借助AVL等辅助查找表。拓扑重建的时间复杂度由原来的O(n log n)降低至O(n)。通过SMF格式文件进行的测试结果表明,在普通PC上重建含有10万个三角面片模型的拓扑结构也只需1s。     

基于奇异值分解的三维网格模型数字水印算法

针对三维网格模型的版权保护提出了一种新的基于奇异值分解(SVD)的数字水印算法。算法利用几何信号处理框架将三维几何信号转换成平面规则采样信号，再用SVD技术嵌入水印。实验结果表明，算法具有较好的透明性和鲁棒性。     

Advancing fan-front: 3D triangle mesh compression using fan based traversal

Connectivity compression techniques for very large 3D triangle meshes are based on clever traversals of the graph representing the mesh, so as to avoid the repeated references to vertices. In this paper we present a new algorithm for compressing large 3D triangle meshes through the successive conquest of triangle fans. The connectivity of vertices in a fan is implied. As each fan is traversed, the current mesh boundary is advanced by the fan-front. The process is recursively continued till the entire mesh is traversed. The mesh is then compactly encoded as a sequence of fan configuration codes. The fan configuration code comprehensively encodes the connectivity of the fan with the rest of the mesh. There is no need for any further special operators like split codes and additional vertex offsets. The number of fans is typically one-fourth of the total number of triangles. Only a few of the fan configurations occur with high frequency, enabling excellent connectivity information compression using range encoding. A simple implementation shows significant improvements, on the average, in bit-rate per vertex, compared to earlier reported techniques.     

3D object recognition based on curvature information of planar views

In this paper, a 3D object recognition algorithm is proposed. Objects are recognized by studying planar images corresponding to a sequence of views. Planar shape contours are represented by their adaptively calculated curvature functions, which are decomposed in the Fourier domain as a linear combination of a set of representative shapes. Finally, sequences of views are identified by means of Hidden Markov Models. The proposed system has been tested for artificial and real objects. Distorted and noisy versions of the objects were correctly clustered together.     

一种新的地物与地形的网格融合方法

三维地形可视化中重要的地物模型需要使用CAD软件（3D Studio MAX/AutoCAD（3D）/MultiGen）构建的模型数据,来逼真表示城市的精细结构、材质特征及地物的内部形态,在将其和地形网格集成的过程中,必须让地物和地形之间实现无缝融合。提出了一种新的地物和地形的融合方法：首先读取地形高度图,利用基于四叉树的LOD技术生成地形网格,其次导入三维地物模型并放置于地形网格某位置,对三维地物模型投影得到地物模型的底面网格边界框及点集,地物边界框对应的地形网格分裂,产生融合位置的地形网格边界及对应点集,根据地物网格边界和地形网格边界的这两个点集以及Delauney三角形限定条件生成三角网,实现网格融合。利用该方法实现了四叉树LOD技术生成的地形和地物的融合,最后讨论了该方法的特点及应用。     

Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

When an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current hole-filling algorithms and the resolution of the image irradiance equations are overcome.     

Three-dimensional optical measurements and reverse engineering for automotive applications

The paper describes a very special and suggestive example of optical three-dimensional (3D) acquisition, reverse engineering and rapid prototyping of a historic automobile, a Ferrari 250 Mille Miglia, performed primarily using an optical 3D whole-field digitiser based on the projection of incoherent light (OPL-3D, developed in our laboratory). The entire process consists in the acquisition, the point cloud alignment, the triangle model definition, the NURBS creation, the production of the STL file, and finally the generation of a scaled replica of the car.The process, apart from the importance of the application to a unique, prestigious historic racing car, demonstrates the ease of application of the optical system to the gauging and the reverse engineering of large surfaces, as automobile body press parts and full-size clays, with high accuracy and reduced processing time, for design and restyling applications.     

基于整体映射的不规则三维模型多细节层次描述

针对无孔洞、有边界的不规则三维模型,提出一种整体映射的多细节层次描述方法：先通过整体映射变换,将三维网格无遮挡、均匀地映射到平面正方形中;再通过正方形中初始网格的自动细化和重采样,得到所需的网格简化模型;获取不同层次简化模型,从而构建多细节层次描述。相对于传统的几何元素删除型网格简化局部型算法,以及新近的基于几何图像描述的整体型算法,该方法算法快速、简单、稳定,描述效果也较好。     

面向道路工程Web3D档案管理的三维可视化方法

道路工程Web3D档案管理技术对辅助提高决策能力具有重要意义。对其中的海量数据组织管理、三维整体建模及模型简化方法进行了研究。提出了基于有向无环图的三维场景组织管理方法,深度方向从总体到细节的逐步细分,广度方向按里程分段或模型类型进行划分,标准模型节点为多个父节点所共享;基于约束Delaunay三角网建立了道路三维整体模型;提出了顾及约束的三维模型简化误差度量准则,考虑了对任意边进行简化时的几何误差,并为约束边建立了一个附加误差项,保证约束边尽早细化。基于上述方法开发了道路工程Web3D档案管理系统,远程客户端可快速重构出三维模型并较好地保留了约束边,目前已应用在多条高速公路的建设、运营管理中。     

An efficient and robust algorithm for 3D mesh segmentation

This paper presents an efficient and robust algorithm for 3D mesh segmentation. Segmentation is one of the main areas of 3D object modeling. Most segmentation methods decompose 3D objects into parts based on curvature analysis. Most of the existing curvature estimation algorithms are computationally costly. The proposed algorithm extracts features using Gaussian curvature and concaveness estimation to partition a 3D model into meaningful parts. More importantly, this algorithm can process highly detailed objects using an eXtended Multi-Ring (XMR) neighborhood based feature extraction. After feature extraction, we also developed a fast marching watershed-based segmentation algorithm followed by an efficient region merging scheme. Experimental results show that this segmentation algorithm is efficient and robust.