基于粒子群优化算法的三角网格孔洞修补

为了对三角网格模型中的复杂孔洞和曲率变化较剧烈部位处的孔洞进行修补,提出了一种基于粒子群优化算法（PSO）的三角网格孔洞修补算法。首先对孔洞多边形进行初始网格化,并计算所有网格顶点的梯度值,然后采用PSO搜索与孔洞边缘顶点梯度匹配的点集,最后根据孔洞匹配点集中顶点的梯度对孔洞中的初始网格进行修正,实现三角网格孔洞的修补。实验表明,该算法对各种复杂或曲率变化较大的孔洞,都有很好的修补效果。     

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.     

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.     

Metamorphosis of arbitrary triangular meshes

Three-dimensional metamorphosis (or morphing) establishes a smooth transition from a source object to a target object. The primary issue in 3D metamorphosis is to establish surface correspondence between the source and target objects, by which each point on the surface of the source object maps to a point on the surface of the target object. Having established this correspondence, we can generate a smooth transition by interpolating corresponding points from the source to the target positions. We handle 3D geometric metamorphosis between two objects represented as triangular meshes. To improve the quality of 3D morphing between two triangular meshes, we particularly consider the following two issues: 1) metamorphosis of arbitrary meshes; 2) metamorphosis with user control. We can address the first issue using our recently proposed method based on harmonic mapping (T. Kanai et al., 1998). In that earlier work, we developed each of the two meshes (topologically equivalent to a disk and having geometrically complicated shapes), into a 2D unit circle by harmonic mapping. Combining those two embeddings produces surface correspondence between the two meshes. However, this method doesn't consider the second issue: how to let the user control surface correspondence. The article develops an effective method for 3D morphing between two arbitrary meshes of the same topology. We extend our previously proposed method to achieve user control of surface correspondence     

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.     

Topological refinement procedures for triangular finite element meshes

This paper presents a topological approach to improve the quality of unstructured triangular finite element meshes. Topological improvement procedures are presented both for elements that are interior to the mesh and for elements connected to the boundary. Optimal ordering of the topology improvement operations and their efficient implementation is also discussed. Several example meshes are included to demonstrate the effectiveness of the approach in improving element quality in a finite element mesh.     

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.     

A local tangential lifting differential method for triangular meshes

In this note we present a local tangential lifting (LTL) algorithm to compute differential quantities for triangular meshes obtained from regular surfaces. First, we introduce a new notation of the local tangential polygon and lift functions and vector fields on a triangular mesh to the local tangential polygon. Then we use the centroid weights proposed by Chen and Wu [4] to define the discrete gradient of a function on a triangular mesh. We also use our new method to define the discrete Laplacian operator acting on functions on triangular meshes. Higher order differential operators can also be computed successively. Our approach is conceptually simple and easy to compute. Indeed, our LTL method also provides a unified algorithm to estimate the shape operator and curvatures of a triangular mesh and derivatives of functions and vector fields. We also compare three different methods : our method, the least square method and Akima’s method to compute the gradients of functions.     

一种3维模型的网格盲水印算法

3维模型的数字水印是数字水印研究的热点之一,鲁棒性、嵌入可读性水印和盲检测是3维模型数字水印的难点所在。从增强3维模型数字水印的鲁棒性出发,提出一种基于局部几何空间的3维模型数字水印算法,它以模型三角网格顶点在其一环邻居顶点为所确定的局部几何空间;通过改变顶点在局部几何空间中的位置来嵌入水印,并以调整其间的夹角来嵌入水印序列的索引,而调整顶点与圆心的距离来嵌入较高比特的二进制数值。本文算法在水印检测时,无需原始模型,且可抵抗平移、旋转、均匀缩放、顶点乱序、剪切及网格简化等攻击。实验结果表明, 该水印算法具有很好的鲁棒性、可读水印的不可感知性和盲水印检测的优势。     

A local tangential lifting differential method for triangular meshes

In this note we present a local tangential lifting (LTL) algorithm to compute differential quantities for triangular meshes obtained from regular surfaces. First, we introduce a new notation of the local tangential polygon and lift functions and vector fields on a triangular mesh to the local tangential polygon. Then we use the centroid weights proposed by Chen and Wu [4] to define the discrete gradient of a function on a triangular mesh. We also use our new method to define the discrete Laplacian operator acting on functions on triangular meshes. Higher order differential operators can also be computed successively. Our approach is conceptually simple and easy to compute. Indeed, our LTL method also provides a unified algorithm to estimate the shape operator and curvatures of a triangular mesh and derivatives of functions and vector fields. We also compare three different methods : our method, the least square method and Akima’s method to compute the gradients of functions.     

三角网格曲面上离散曲率改进算法

计算三角网格离散曲面曲率的Meyer方法几何意义简明,计算量较小,但其计算效果仍有进一步提高的潜力。通过对Meyer方法的深入分析,提出了平均曲率构造向量和Gauss曲率构造角的概念,并指出了它们的几何意义,在此基础上构造了对Meyer方法的改进算法。经分析,提出的改进算法精简了各个主要计算步骤,避免了不必要的计算误差。仿真计算结果表明,改进算法是有效的,提高了三角网格离散曲率的计算精度和计算效率。     

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.     

任意三角网格模型体积的快速精确计算方法

三角网格是使用最为广泛的网格模型。提出了一种仅根据三角网格模型的三角面片集合计算模型体积的方法。该方法通过指定投影平面,计算每个三角面片及其在投影平面上的投影所围成的凸五面体的带符号体积（必要时对三角面片进行细分）,整个模型的体积为所有凸五面体带符号体积的代数和。所提出的三角网格模型体积计算方法能实现模型体积的快速准确计算。在大型水电工程施工模拟中施工单元的方量计算测试和不同规模的三角网格模型体积计算测试都证实了该方法的有效性。     

An efficient algorithm for characteristic tracking on two-dimensional triangular meshes

Tracking characteristics on unstructured meshes is an important part of many numerical methods in computational fluid mechanics. In this paper, we propose an efficient algorithm for characteristic tracking on two-dimensional unstructured triangular meshes. Numerical experiments, including an example for applying this algorithm with the Eulerian-Lagrangian localized adjoint method (ELLAM) to solve a convection-dominated convection-diffusion problem, are presented to demonstrate the efficiency of this algorithm.     

Aesthetic and functional analysis for product model validation in reverse engineering applications

Reverse engineering techniques are broadly used in the development process of products with meaningful aesthetic properties. Many stylists prefer to evaluate the product shape on the basis of a full-scale hand made physical mock-up. Such model has then to be converted into a 3D CAD model, to begin the product engineering and production processes.A critical aspect of the RE process is that the physical mock-up, made by the stylist, usually does not take into account the engineering production constraints. The surface reconstruction activity must then be followed by a modelling phase, where the engineering designer modifies the reconstructed model shape in order to make it suitable for production.At the end of this process, no matter how accurate and precise the surface reconstruction phase has been, the product model will be different from the original mock-up, and then it needs to be submitted to the stylist for the validation of its shape.For the stylist, getting used to working with physical models, the shape validation on a virtual model is not a trivial task.The objective of this research is to develop a software tool to support the identification of aesthetic and functional regions of the product model shape, that have been modified with respect to the original mock-up.The proposed approach is based on the decomposition of a 3D surface analysis problem into a simpler 2D curves analysis problem. This approach simulates the traditional method used by stylists to evaluate the quality of shapes.The implementation of the developed algorithms has been performed using a commercial software package (I-deas FreeForm by EDS/Unigraphics) and it has been successfully applied on real test cases.     

Digitizing uncertainty modeling for reverse engineering applications: regression versus neural networks

The coordinate measuring machine is one of the two types of digitizers most popularly used in reverse engineering. A number of factors affect the digitizing uncertainty, such as travel speeds of the probe, pitch values (sampling points), probe angles (part orientations), probe sizes, and feature sizes. A proper selection of these parameters in a digitization or automatic inspection process can improve the digitizing accuracy for a given coordinate-measuring machine. To do so, some empirical models or decision rules are required. This paper applies and compares the nonlinear regression analysis and neural network modeling methods in developing empirical models for estimating the digitizing uncertainty. The models developed in this research can aid error prediction, accuracy improvement, and operation parameter selection in computer-aided reverse engineering and automatic inspection.