基于逆√3细分的渐进网格生成算法研究

提出一种基于逆√3细分的渐进网格生成算法,用于解决图形的快速传输和显示问题.算法的基本思路是:将细密网格通过边折叠操作得到简化网格,以细分极限点逼近原始网格为准则进行网格调整,采用√3细分得到高密度网格,调整后进行逆√3细分,即逐层次删除部分顶点,生成用于重构渐进网格模型的基网格,并记录每层删除顶点在采用本层表示时相对于细分计算位置的几何调整量.√3细分过程中三角片数量增长速度较慢,采用逆√3细分利于生成多层次的渐进网格,经实例验证,逆√3细分生成渐进网格的效果能满足快速、多分辨率显示要求.     

一种可调的Catmull-Clark细分曲面

通过在曲面细分过程中引入一个参数t(0≤t≤1)，使得Catmull-Clark细分曲面可调，得出一种新的算法。这种算法简单直观，通过调节参数t值，可以得到一族细分曲面。该族细分曲面不但保留了许多Catmull—Clark细分曲面的特性，而又可以方便地解决在工程中经常遇到的调整曲面位置和形状的问题。同时，还可以将这种细分算法作为Catmull-Clark细分的前置处理方法。文中详细讨论了这一算法，并给出了验证实例。     

Butterfly细分曲面的快速求值

从分析Butterfly细分曲面的局部参数化出发,通过参数二进制分解生成数列以及构造细分格式的局部加细矩阵,并利用对应矩阵序列乘积与矩阵特征分解计算出控制点权值,从而解决TButterfly细分曲面插值问题.算法独立于网格存储的数据结构,避免了求邻接关系等费时的操作,并且容易推广到其他三角网格插值细分格式的曲面求值中.     

向量线性相关的三角网格自适应Loop细分方法

根据过同一起点,且线性相关的三个向量在同一平面上的原理提出了一种新的三维表面自适应Loop细分算法,即对网格模型过同一顶点1邻域上的所有三个紧邻边组成的三个向量判断其是否线性相关来断定该顶点的1邻域是否平坦,从而进一步判断该顶点是否参与细分.但是三角网格模型上的三条边不可能都严格地在同一个平面上,当这些向量组成的行列式值趋于零时,便认为它们在同一平面上.实验表明,该方法减少了细分的数据量和处理速度.     

网格细分技术在汽车外形设计中的应用

细分造型技术因其计算规则简单、可以表示任意拓扑特性和几何特征的曲面等性质,受到造型技术领域中众多学者的关注,为复杂的汽车外形设计提供了工具.该文阐释了网格细分方法的基本思想以及两类典型的细分模式,提出了在相关几何造型、有限元分析和动态仿真软件配合下,设计复杂汽车外形曲面的细分技术方案;对车体曲面的控制网格生成、边界限定等关键技术进行了讨论.利用文中方法可以有效地缩短复杂汽车外形曲面的造型、计算和分析时间,为汽车外形设计的逆向工程应用提供方法和工具.     

用Catmull-Clark细分及网格调整方法重构牙齿曲面

首先根据牙齿表面测量数据点,计算出其长方体包围盒;并据此构造细分曲面的初始网格;采用矩阵对角化方法,推导Catmull-Clark细分极限点的表达式,计算初始网格的顶点经过细分后的极限点;按照极限点逼近数据点的原则移动控制网格顶点,经过逐次再细分、再调整网格,使各级网格在数据点的＂引导＂下逐步变形,使网格逐步逼近牙齿表面的测量数据点集合,实现牙齿表面模型的三维重建。     

基于Catmull-Clark细分规则的双参数细分曲面

通过在曲面细分过程中引入两个参数,给出一种新的细分曲面构造的算法,使得所得的细分曲面可调.通过调节一个参数值,可以得到一族细分曲面.另一个参数是细分过程的改变参数,改变它的初值,也可得细分结果.最后给出了曲面设计的实例,表明这种算法简单、有效.     

Loop细分曲面的加工等距面生成及误差控制算法

不同层次的Loop细分网格曲面可作为不同工序的加工模型.当判断各细分层次与极限曲面的整体误差时,若不考虑所存在的尖锐特征,则计算所得误差将高于实际误差.本文考虑了尖锐特征的存在,对现有给定误差估计所需细分次数的算法进行了改进,并针对粗加工和精加工的不同特点,给出了各工序等距面的生成及调整算法.实践验证方法可行.     

一种Loop细分小波的边界处理方法

细分小波近年来发展迅速,在计算机图形显示、渐进网格传输和网格多分辨率编辑等领域获得了广泛的应用。Bertram提出的Loop细分小波是基于提升格式的双正交细分小波的典型范例,它所针对的对象均为网格的内部顶点。目前尚未发现相关文献提及细分小波对于边界的处理。该文在Loop细分小波算法的基础上,给出了一种Loop细分小波边界处理的方法,经验证效果令人满意。     

基于细分模式与能量优化的曲面混合方法

论述了用Catmull-Clark细分曲面及能量优化法对多张三次B样条曲面进行混合的方法。首先引入一种边界拓扑修改的细分规则，可生成逐段光滑的细分曲面，在此基础上构造多张三次B样条曲面的混合曲面，采用能量优化方法求解控制顶点。与现有方法相比，构造的混合曲面形状易于控制，能满足复杂的边界要求，且整个混合曲面除了在有限奇异点处为C^1连续外均达到C^2连续。     

A new volume warping method for surface reconstruction

Volumetric models of 3D objects have recently been introduced into the reverse engineering process. Due to their efficiency and simplicity, grid-based methods are considered the major technique for reconstructing surfaces from these volumetric models. Yet these methods suffer from a number of inherent drawbacks, resulting from the fact that the imposed Cartesian grid is generally not well adapted to the surface in size or in orientation. To overcome the above obstacles, this paper proposes a new iso-surface extraction method for volumetric objects. The main idea is first to construct a geometrical field induced by the object's shape. This geometrical field represents the natural directions and grid cell size for each point in the domain. Then, the imposed volumetric grid is deformed by the produced geometrical field to approach the object's shape. The iso-surface meshes can be extracted from the resulting adaptive grid by any conventional grid-based contouring technique. These meshes provide a better approximation of the unknown surface and exhibit the anisotropy present in this surface. Since the produced meshes are all quad, Catmull–Clark subdivision surfaces can be directly constructed from them. Moreover, accurate physical models of the reconstructed objects can be produced using rapid prototyping (RP) technology.     

A new volume warping method for surface reconstruction

Volumetric models of 3D objects have recently been introduced into the reverse engineering process. Due to their efficiency and simplicity, grid-based methods are considered the major technique for reconstructing surfaces from these volumetric models. Yet these methods suffer from a number of inherent drawbacks, resulting from the fact that the imposed Cartesian grid is generally not well adapted to the surface in size or in orientation. To overcome the above obstacles, this paper proposes a new iso-surface extraction method for volumetric objects. The main idea is first to construct a geometrical field induced by the object's shape. This geometrical field represents the natural directions and grid cell size for each point in the domain. Then, the imposed volumetric grid is deformed by the produced geometrical field to approach the object's shape. The iso-surface meshes can be extracted from the resulting adaptive grid by any conventional grid-based contouring technique. These meshes provide a better approximation of the unknown surface and exhibit the anisotropy present in this surface. Since the produced meshes are all quad, Catmull-Clark subdivision surfaces can be directly constructed from them. Moreover, accurate physical models of the reconstructed objects can be produced using rapid prototyping (RP) technology.     

A surface mesh smoothing and untangling method independent of the CAD parameterization

A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to check the quality and validity of a surface mesh. Then, we detail how to optimize any Jacobian-based distortion measure to obtain smoothed and untangled meshes with the nodes on the surface. We prove that this method is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations. The examples show that the method can optimize meshes composed by a large number of inverted elements. Finally, the method can be extended to obtain high-order meshes with the nodes on the CAD surfaces.     

Automatic registration for inspection of complex shapes

With the increase in computing power, new ways of inspecting manufactured parts can be realized. The availability of computing power allows computational alignment between measurements and computer aided design (CAD) models using registration algorithms. The present paper proposes a new inspection approach that removes a constraint of traditional inspection processes related to part alignment. Traditional techniques require a fixture to align the part so the inspection machine can establish a common coordinate system between the measurement and the CAD model. Removing the need of a fixture aids automating the inspection process. The proposed approach employs an automated registration methodology based on two main stages. First, a part measurement in an arbitrary coordinate system is transformed to approximately fit the shape of the CAD model. Then, this approximation is iteratively refined until its convergence. To demonstrate the feasibility of the proposed method, results are demonstrated on measurements obtained from three rapid prototyped parts with complex geometry.     

Automatic registration for inspection of complex shapes

With the increase in computing power, new ways of inspecting manufactured parts can be realized. The availability of computing power allows computational alignment between measurements and computer aided design (CAD) models using registration algorithms. The present paper proposes a new inspection approach that removes a constraint of traditional inspection processes related to part alignment. Traditional techniques require a fixture to align the part so the inspection machine can establish a common coordinate system between the measurement and the CAD model. Removing the need of a fixture aids automating the inspection process. The proposed approach employs an automated registration methodology based on two main stages. First, a part measurement in an arbitrary coordinate system is transformed to approximately fit the shape of the CAD model. Then, this approximation is iteratively refined until its convergence. To demonstrate the feasibility of the proposed method, results are demonstrated on measurements obtained from three rapid prototyped parts with complex geometry.     

颗粒流体系统Euler/Lagrange模型中自适应三角网格的生成

针对二维颗粒流体系统Euler／Lagrange模型的有限元模拟,建立了三角网格生成的自适应算法。该算法能够根据颗粒分布与颗粒大小自适应地调整网格的疏密程度,使其网格密度在系统边界附近及颗粒边缘附近较大,而在其它地方较小。与此同时,网格的光滑化也提高了网格质量, 从而为颗粒流体系统介观尺度的有限元模拟奠定了基础。     

Rapid prototyping through scanned point data

Rapid prototyping (RP) is an emerging, non-traditional fabrication method and has been recognized as a valid tool to shorten the lead-time from design to manufacture effectively. Most of the current RP systems adopt the triangular meshes of stereolithoraphy (STL) as a standard format for data input. Thus, the construction of triangular meshes directly affects the quality of RP parts and their subsequent processes. Traditionally, STL data are output from 3D CAD models built using commercial 3D CAD/CAM software packages. This study, however, differs from the traditional way in that it generates the STL data directly from scanned 3D data points, thus preventing various problems associated with 3D CAD modelling from a large quantity of data points. Specific tasks involved in this study include: (1) development of the methodology to convert massive data points into numerous, connected triangular meshes, (2) determination of unit normal vector for each triangular mesh facet, (3) output of triangular meshes with normal vectors in STL format, and (4) slicing of triangular-mesh model into a series of 2D sections.     

Virtual hybrid-FDM system to enhance surface finish

Many rapid prototyping systems which produce prototypes by layer-by-layer material deposition are now commercially available. The layer-by-layer deposition process leads to a stepped surface known as staircase. Staircase formation is a geometric constraint of the layered manufacturing, which can not be eliminated. The presence of staircase on the surface of a prototype detracts from the surface finish and hence restricts functionality of prototypes. It is realized that there is a need to make modifications in RP (rapid prototyping) systems so that prototypes with better surface finish can be produced without incurring high production costs. A virtual hybrid fused deposition modelling system (hybrid-FDM) is proposed in the present work that uses both layer-by-layer deposition and machining. In this system, CAD model is sliced adaptively using limited centre line average (Ra) value as a criterion (Pandey et al. 2003a). Hot cutter machining/ploughing (HCM) (Pandey et al. 2003b) is recommended to machine the build edges (staircase) of ABS material. Numerically controlled x-y traversing mechanism is proposed as an attachment to move hot cutters along the periphery of slices to machine build edges. In this paper, geometrical designs of cutters are proposed. A process planning system to decide the number of layers to be deposited and then machined in order to access intricate features of a part is implemented. The developed system simulates surface roughness, before and after hot cutter machining. An experimental study is carried out by machining the build edges of an axisymmetric FDM part on lathe machine to form a basis for a hybrid-FDM system.     

Decision support system for rapid prototyping process selection through integration of fuzzy synthetic evaluation and an expert system

A new method is proposed for selecting the most appropriate rapid prototyping process according to user's specific requirements by using the expert system and fuzzy synthetic evaluation. The selection process is divided into two stages. First, it is necessary to generate feasible alternatives, which are executed under the expert system environment. Second, given those feasible alternatives, the fuzzy synthetic evaluation approach is employed to produce a ranking order of the alternatives and to finalize the most suirapid prototyping system. One distinctive characteristic of this method is that quantitative as well as qualitative measures are employed, providing more accurate results. The decision system developed based on the proposed method is composed of four modules: a database to store the specifications of various rapid prototyping processes; a knowledge-based expert system for determining the feasible alternatives; a fuzzy synthetic evaluation model to select the most suitable rapid prototyping process; and a user interface and an expert interface to interact with the system. The fuzzy synthetic evaluation approach used in the system is illustrated in detail by a numerical example. Furthermore, a Java-enabled solution, together with web techniques, is employed for developing such a networked decision support system. Finally, two examples of rapid prototyping process selection are designed to demonstrate the application of the system. The system has been implemented and can run at a rapid prototyping and manufacturing networked service platform that the authors have developed.     

Laser metal forming processes for rapid prototyping - A review

In the current rapid prototyping processes, a physical part of a computer model can be quickly produced for functional and dimensional verification. Most of the existing systems can only produce non-metal parts, and thus limit rapid prototyping applications. The laser-based metal forming process is a technique that has the potential to produce fully functional models directly from a CAD system and eliminate the need for an intermediate step. This paper presents a review of the state of the art laser metal forming (LMF) processes. LMF process hardware, software, and process parameters are discussed, including laser parameters, beam delivery systems, work table variables, metal deposition techniques, measurement, and control. Process limitations, materials, and costs are summarized.